Preface

Wel­come to our new online text­book on fore­cast­ing. This book is intended as a replace­ment for Makri­dakis, Wheel­wright and Hyn­d­man (Wiley 1998).

The entire book is avail­able online and free-of-charge. Of course, we won’t make much money doing this, but text­books never make much money any­way — the pub­lish­ers make all the money. We’d rather cre­ate some­thing that is widely used and use­ful, than have large pub­lish­ers profit from our efforts.

Even­tu­ally a print ver­sion and a down­load­able e-version of the book will be avail­able to pur­chase on Ama­zon, but not until a few more chap­ters are written.

This text­book is intended to pro­vide a com­pre­hen­sive intro­duc­tion to fore­cast­ing meth­ods and present enough infor­ma­tion about each method for read­ers to use them sen­si­bly. We don’t attempt to give a thor­ough dis­cus­sion of the the­o­ret­i­cal details behind each method, although the ref­er­ences at the end of each chap­ter will fill in many of those details.

The book is writ­ten for three audi­ences: (1) peo­ple find­ing them­selves doing fore­cast­ing in busi­ness when they may not have had any for­mal train­ing in the area; (2) under­grad­u­ate stu­dents study­ing busi­ness; (3) MBA stu­dents doing a fore­cast­ing elec­tive. We use it our­selves for a second-year sub­ject for stu­dents under­tak­ing a Bach­e­lor of Com­merce degree at Monash Uni­ver­sity, Australia.

For most sec­tions, we only assume that read­ers are famil­iar with alge­bra, and high school math­e­mat­ics should be suf­fi­cient back­ground. Read­ers who have com­pleted an intro­duc­tory course in sta­tis­tics will prob­a­bly want to skip some of Chap­ters 2 and 4. There are a cou­ple of sec­tions requir­ing knowl­edge of matri­ces, but these are flagged.

At the end of each chap­ter we pro­vide a list of “fur­ther read­ing”. In gen­eral, these lists com­prise sug­gested text­books that pro­vide a more advanced or detailed treat­ment of the sub­ject. Where there is no suit­able text­book, we sug­gest jour­nal arti­cles that pro­vide more information.

We use R through­out the book and we intend stu­dents to learn how to fore­cast with R. R is free and avail­able on almost every oper­at­ing sys­tem. It is a won­der­ful tool for all sta­tis­ti­cal analy­sis, not just for fore­cast­ing. See Using R for instruc­tions on installing and using R.

The book is dif­fer­ent from other fore­cast­ing text­books in sev­eral ways.

  • It is free and online, mak­ing it acces­si­ble to a wide audience.
  • It uses R which is free, open-source, and extremely pow­er­ful software.
  • It is con­tin­u­ously updated. You don’t have to wait until the next edi­tion for errors to be removed or new meth­ods to be dis­cussed. We will update the book frequently.
  • There are dozens of real data exam­ples taken from our own con­sult­ing prac­tice. We have worked with hun­dreds of busi­nesses and orga­ni­za­tions help­ing them with fore­cast­ing issues, and this expe­ri­ence has con­tributed directly to many of the exam­ples given here, as well as guid­ing our gen­eral phi­los­o­phy of forecasting.
  • We empha­sise graph­i­cal meth­ods more than most fore­cast­ers. We use graphs to explore the data, analyse the valid­ity of the mod­els fit­ted and present the fore­cast­ing results.

Use the table of con­tents on the right to browse the book. If you have any com­ments or sug­ges­tions on what is here so far, feel free to add them below.

Happy fore­cast­ing!

Rob J Hyn­d­man
George Athana­sopou­los
April 2012.

Pro­ceed to Chap­ter 1

  • Troy Lynch

    Thank you, Rob and George, for putting together this FPP. I have been through chap­ters 1, 3, 5 and 6 (or what was avail­able) and find it quite help­ful. I went back and had a look at the 1998 text. As a poten­tial prac­ti­tioner of these tools, I think that what you have put together in the FPP (and what I have seen of the the 1998) are really straight­for­ward ways of deal­ing with forecasting.

    I par­tic­u­larly like the step-by-step man­ner you use to build up the edi­fice of dif­fer­ent mod­els with­out get­ting too bogged down in econo­met­ric the­ory. (I also appre­ci­ate the chap­ter 11 dis­cus­sion in your 1998, which I have partly fol­lowed in some of the jour­nal arti­cles, that exam­ines the use, accu­racy and and sat­is­fac­tion of dif­fer­ent mod­els. I gather the sim­pler the bet­ter but com­bi­na­tions also work well.)

    It is a great and gen­er­ous ges­ture for you chaps to put the FPP up on your site for “free”. I hope that you con­tinue to add to and com­plete the FPP. It will prove to be a great resource.

    Cheers
    Troy.

  • Wei

    Thanks for authors’ efforts to make this gem freely avail­able online. I would very much like to chip-in some $ if you add a “Chip-in” link for this book.

    Your efforts are so appre­ci­ated and should be rewarded.

    • http://robjhyndman.com Rob J Hyndman

      Thanks for the vote of con­fi­dence. We’ll set some­thing up for dona­tions when the site is closer to completion.

  • Jose J. Hernandez

    George, Rob

    Your effort sets an exam­ple of new ways for the dif­fu­sion of knowl­edge. I also appre­ci­ate how you focus on acces­si­bil­ity for stu­dents and prac­ti­tion­ers. Thanks and wish you suc­cess in this project

    Jose

  • Mario Tejada Harsanyi

    You guys are AMAZING! con­grat­u­la­tions from Mexico!…yeah put some “chip-in” to coop­er­ate with some $, its a big effort. Best wishes!

  • Mario Tejada Harsanyi

    I got to this page by googling : makri­dakis wheel­wright and hyn­d­man r code, but where is the link to get to this page from professor’s Hyn­d­man website?

    Maybe not many peo­ple have seen this site.

    Greets.

    • http://robjhyndman.com Rob J Hyndman

      We will be pub­li­ciz­ing the site when it is closer to completion.

  • Doug

    Thanks, I just learned about your book at ama­zon today. Do you have any advanced math require­ment for read­ing the text?

    • http://robjhyndman.com Rob J Hyndman

      An intro­duc­tory course in sta­tis­tics would be use­ful, but we do try to cover the back­ground mate­r­ial in any case. Oth­er­wise, high school math­e­mat­ics should be suf­fi­cient for most chap­ters. There are a cou­ple of sec­tions requir­ing knowl­edge of matri­ces, but these are flagged.

  • Ther­i­malaya

    Thank you for this book, this is very use­ful and you have used the r-package so that stu­dent like me can learn the pack­age along with the forecasting.

    I want to ask one ques­tion? Are those graphs are ren­dered online or are placed there as image?

    • http://robjhyndman.com Rob J Hyndman

      All the graph­ics here are images cre­ated on my PC and uploaded. You should get iden­ti­cal results if you use the R code that accom­pa­nies most figures.

  • Eric

    Rob, looks great so far.

    One minor sug­ges­tion for the pref­ace would be to add a com­ment on who the tar­geted audi­ence might be and the expected level of math­e­mat­i­cal sophis­ti­ca­tion required

    • http://robjhyndman.com Rob J Hyndman

      Thanks for the sug­ges­tion. I’ve now added a cou­ple of para­graphs of explanation.

  • dmon­der

    This is won­der­ful. I look for­ward to read­ing through this book and learn­ing about forecasting.

    FYI: In the text quoted below, I think you meant “want to skip” in this sentence.

    “Read­ers who have com­pleted an intro­duc­tory course in sta­tis­tics will prob­a­bly want so skip some of Chap­ters 2 and 4.”

    Thank you for this resource!
    David

    • http://robjhyndman.com Rob J Hyndman

      Thanks. Error now fixed.

  • http://pulse.yahoo.com/_3NOMIDA6UZ6LNXUGCTEZSWBQOY Bug­gy­Fun­Bunny

    The qual­ity of book pub­lish­ing has got­ten pretty bad. If you get to the point of mak­ing a real book, please choose either (what passes for) hard­cover or Rep-Kover (what O’Reilly used to do). A hinged spine is use­ful both for humans and books.

    • http://robjhyndman.com Rob J Hyndman

      I don’t know why you think the online ver­sion isn’t “real”! In any case, there will be a print ver­sion, hope­fully by Jan 2013. Thanks for the suggestions.

  • Edward Choh

    Is a PDF ver­sion avail­able? Even if the mate­r­ial is in-progress?

    • http://robjhyndman.com Rob J Hyndman

      We will make an e-version avail­able (but not pdf) at the same time as the print ver­sion. In the mean­time, it is avail­able online only.

  • Cas­ton Sigauke

    Thank you Rob and George for the won­der­ful work which you are freely giv­ing to stu­dents, aca­d­e­mics and prac­ti­tion­ers in the field of demand fore­cast­ing. may the almighty richly bless you and give you more energy to con­tinue work­ing on this project.

  • JB

    I have just recently been look­ing at pur­chas­ing a book on this topic — and here you are (well get­ting there at least).

    This is great — it makes qual­ity con­tent avail­able to peo­ple regard­less of their abil­ity to pay.

    Speak­ing of which, in the pref­ace you state “Of course, we won’t make much money doing this, but text­books never make much money any­way — the pub­lish­ers make all the money.” Given that I and many oth­ers that will use this book fall into the “able to pay” cat­e­gory — it would be use­ful to have a sug­gested dona­tion or may be a bench­mark based on the amount you would receive if pub­lish­ing in the tra­di­tional fash­ion. That way I would feel I am pay­ing a fair price.

  • Phillip Screw­driver

    This is good! I am not a fore­cast­ing pro­fes­sional, but use the con­cepts in my job, and really have enjoyed learn­ing to use your [b]forecast[/b] pack­age in R.

    I look for­ward to read­ing this.

  • Gad

    Thanks for the book. Just won­der­ing how to use sam­ple data. I loaded library(fpp). but when i typed credit, i got error:
    Error: object ‘credit’ not found

    Thanks

    Gad

    • http://robjhyndman.com Rob J Hyndman

      It works for me. It sounds like fpp is not load­ing for you. Or per­haps you have a very old ver­sion of fpp.

  • Andrew Z

    In 7/7 there is a space miss­ing between two words in the sen­tence, “For this model, we assume thatone-step fore­cast errors are given by ”

  • Andrew Z

    I am read­ing chap­ters 7 and 8 and am not clear on the dis­tinc­tion between trend, level, and slope. I don’t see a glos­sary, and the site search is not help­ful because it isn’t in order. It may be nice to have these explained in one place with examples.

    I admit I went quickly through the for­mu­las, and now look­ing at fig­ure 7.4 it’s con­fus­ing to see a flat and neg­a­tive slopes for sheep in Asia.

    • http://robjhyndman.com Rob J Hyndman

      Thanks for the feed­back. We will add some fur­ther expla­na­tion to the chap­ter. The slopes are the slopes of the trend, so a con­stant slope means a lin­ear trend. The decreas­ing slope means the trend is lev­el­ling off, not that it is negative.

      A glos­sary is planned, but won’t be added here until later this year.

      • Andrew Z

        Thank you. That makes sense. So if the trend were already flat and the slope were neg­a­tive, the trend is decreasing.

  • New

    Could you please add some dis­cus­sion on the rela­tion­ship between sta­tis­ti­cal sig­nif­i­cance and fore­cast­ing? For exam­ple, should one select the pre­dic­tors based on sta­tis­ti­cal significance?

  • New

    In sec­tion 5/7, there is a dis­cus­sion as follows.

    “Fore­casts will be unre­li­able if the val­ues of the future pre­dic­tors are out­side the range of the his­tor­i­cal val­ues of the pre­dic­tors. For exam­ple, sup­pose you have fit­ted a regres­sion model with pre­dic­tors X and Z which are highly cor­re­lated with each other, and sup­pose that the val­ues of X in the fit­ting data ranged between 0 and 100. Then fore­casts based on X>100 or X<0 will be unre­li­able. It is always a lit­tle dan­ger­ous when future val­ues of the pre­dic­tors lie much out­side the his­tor­i­cal range, but it is espe­cially prob­lem­atic when mul­ti­collinear­ity is present.”

    Could you please pro­vide any lit­er­a­ture ref­er­ence for this claim? I am think­ing about a coin­te­gra­tion regres­sion where the pre­dic­tor is unit root non­sta­tion­ary. In that case, it is highly likely that the pre­dic­tors may take future val­ues that are out­side of the range pre­vi­ously observed. But it is hard for me to imag­ine that one would argue fore­casts would be unre­li­able in such a case.

    • http://robjhyndman.com Rob J Hyndman

      In chap­ter 5, we are con­sid­er­ing stan­dard regres­sion where the pre­dic­tors are assumed non-random. If the pre­dic­tors are non­sta­tion­ary, they should be dif­fer­enced before fit­ting a regres­sion model. This is dis­cussed in chap­ter 9.

      We will be adding some fur­ther read­ing sec­tions to the end of each chap­ter even­tu­ally. For now, a ref­er­ence on mul­ti­collinear­ity and pre­dic­tion that is help­ful is Askin (J.Forecasting, 1982).

      • New

        Thanks for the reply. I can wait for Chap­ter 9.
        But that “If the pre­dic­tors are non­sta­tion­ary, they should be dif­fer­enced before fit­ting a regres­sion model” struck me as quite out of date.
        Why are you dis­re­gard­ing the lit­er­a­ture on fore­cast­ing using coin­te­grated sys­tems? Is the lit­er­a­ture not con­vinc­ing enough?

  • William

    rob & george. thank you. thank you for tak­ing the mid­dle man out of the dis­tri­b­u­tion of knowledge.

    I’m sur­prised to see a chap­ter on neural net­works. I thought neural net­works were more in the domain of “data min­ing” and “machine learn­ing” than fore­cast­ing. How­ever, I believe that the lines are blurry between learn­ing, data min­ing, and fore­cast­ing. After all, they all seek to make accu­rate predictions.

    I was won­der­ing if you will spend some time on “ran­dom forests”. This method tends to per­form incred­i­bly well in the Kag­gle competitions.

    http://blog.kaggle.com/2012/05/01/chucking-everything-into-a-random-forest-ben-hamner-on-winning-the-air-quality-prediction-hackathon/

    • http://robjhyndman.com Rob J Hyndman

      Neural net­works are used for pre­dic­tion, so they are rel­e­vant. They arose in the data mining/machine learn­ing com­mu­nity, rather than in sta­tis­tics or econo­met­rics. They are some­times accu­rate, but not as often as enthu­si­asts think.

      We may include a chap­ter on bag­ging, boost­ing, ran­dom forests, etc. at some later stage, but it is not planned for 2012.

  • stesch

    This book is fan­tas­tic! I have been look­ing for some­thing like this for a while. One com­ment: the fig­ures are not vis­i­ble using an iPad/iPhone, which is quite an incon­ve­nience for an elec­tronic text­book. Any idea why? Per­haps due to the large res­o­lu­tion of the figures?

    • http://robjhyndman.com Rob J Hyndman

      Hi Stesch. I’m aware of the prob­lem and I’m try­ing to fig­ure out what is caus­ing it. So far I haven’t tracked it down, but hope­fully it will fixed soon.

  • New

    Thanks, Rob, for your reply about the use of sta­tis­ti­cal sig­nif­i­cance to select variables.

    The usual argu­ment against that is the col­in­ear­ity among pre­dic­tors, as you also men­tioned in that sec­tion. But what if my vari­ables are orthog­o­nal (hypo­thet­i­cally)? Is there any lit­er­a­ture that argues p val­ues are not appro­pri­ate even in that case?

    • http://robjhyndman.com Rob J Hyndman

      The p-values are more use­ful in that case, but they still answer the wrong ques­tion. P-values tell you what vari­ables explain the his­tor­i­cal data. They are not nec­es­sar­ily the same vari­ables as best pre­dict future data.

  • New

    Rob, your com­ment that “If the pre­dic­tors are non­sta­tion­ary, they should be
    dif­fer­enced before fit­ting a regres­sion model” struck me as quite out of
    date.
    Why are you dis­re­gard­ing the lit­er­a­ture on fore­cast­ing using coin­te­grated sys­tems? Is the lit­er­a­ture not con­vinc­ing enough? Thanks!

    • http://robjhyndman.com Rob J Hyndman

      Coin­te­gra­tion mod­els are beyond the scope of what we cover in chap­ter 5 and 9/1. If you don’t fit coin­te­gra­tion mod­els, you need to dif­fer­ence all vari­ables to remove non­sta­tion­ar­i­ties. We may include a sec­tion on coin­te­gra­tion later.

      • New

        Thanks, Rob, for your reply. I would sug­gest that you at least men­tion the pos­si­bil­ity of coin­te­gra­tion there. To say cat­e­gor­i­cally that non­sta­tion­ary vari­ables “should be dif­fer­enced before fit­ting a regres­sion model” can be mis­lead­ing. Thanks again.

  • GG

    Typos, miss­ing info, etc on Chap­ter 2

    In sec­tion 2/2, R code for Fig­ure 2.9, the dataset should be “aus­beer” and not “beer”.

    In prob­lem 1 of 2/Exercises, it is not clear which datasets of “fma” are used. I had to do library(help=fma) and fig­ure them out. It would be nice if you could add the names of the spe­cific datasets.

    In prob­lem 3 of 2/Exercises, it not clear what you are ask­ing in 3(d). It would be help if you could rephrase the ques­tion. Also, the com­mand “fcast” couldnt be found for ques­tions 3(g) and 3(h).

    I went through Chap­ters 1 & 2 and the mate­r­ial is great!
    Thanks for all your efforts!

    • http://robjhyndman.com Rob J Hyndman

      Thanks for the com­ments.
      1. aus­beer now fixed.
      2. I delib­er­ately left this out to force stu­dents to learn how to search the index and so they would see what other data were avail­able.
      3. (g) and (h) now fixed. I’m not sure how to make 3(d) any clearer with­out pro­vid­ing the answer.

  • GG

    Typos, etc. in Chap­ter 4

    I think in 4/4, the 2nd line for the R code for Fig 4.4 should read
    plot(jitter(res) ~ jitter(City), ylab=“Residuals”, xlab=“City”, data=fuel)

    In 4/5, the R code at the end of the sec­tion (plot(fcast,.…)) works only in 2.15.1 and not in 2.13 (I am using Win­dows + Rstudio)

    In 4/8, the R code for Fig 4.11 is pro­duc­ing a dif­fer­ent fig­ure from that shown in 4.11. I am not sure whether its a prob­lem with my set­tings or some­thing else.

    Thanks for the mate­r­ial. It is clear and very helpful.

    • http://robjhyndman.com Rob J Hyndman

      Thanks. First prob­lem fixed.

      On the other two, you need to be using a recent ver­sion of the fore­cast pack­age. It’s not the R ver­sion that mat­ters so much as the ver­sion of the fore­cast pack­age that is used, although the most recent ver­sions of the fore­cast pack­age require Rv2.14.0 or later. Please update your sys­tem. The most recent fore­cast pack­age is v3.24.

    • GG

      Also in the R code for Fig 4.12, the last 2 lines should have “fit.ex4” instead “fit”

      • http://robjhyndman.com Rob J Hyndman

        Now fixed.

  • Sandy Hen­der­son

    Rob, and George

    Thanks for this resource. It’s been very useful.

    In the fore­cast­ing sec­tion of the ARIMA mod­els, I think it would be help­ful to make clear that the past errors come from the process of fit­ting the ARIMA model. This wasn’t clear to me at first and the penny dropped when I looked at Chap­ter 7.8 of Makri­dakis, Wheel­wright and Hyn­d­man (Wiley 1998).

    Some­thing along the lines of :
    On the right hand side of the equa­tion, replace future obser­va­tions by their fore­casts, future errors by zero, and past errors by the cor­re­spond­ing resid­u­als obtained dur­ing the model fit­ting process.

  • New

    Rob and colleagues,this
    looks excel­lent! As a social sci­en­tist inter­ested in eval­u­a­tion research, I found the last book extremely help­ful in teach­ing me time
    series meth­ods pretty much from scratch. A cou­ple of sug­ges­tions for your ARIMA
    sec­tions if you haven’t already cov­ered them. In the pre­vi­ous book I found the
    “Inter­ven­tion analy­sis” sec­tion in chap­ter 8 very help­ful. Do you plan to expand on how to use the var­i­ous
    trans­fer func­tion mod­els rec­om­mended in McCleary and Hay (1980) (i.e. abrupt
    per­ma­nent, grad­ual per­ma­nent, and abrupt tem­po­rary mod­els)? Sec­ondly, I fre­quently get asked about sta­tis­ti­cal power for ARIMA
    inter­ven­tion analy­sis, if you are able to com­ment on this in the book then this would
    be very help­ful indeed. Many thanks for this, it looks like a great resource!

    • http://robjhyndman.com Rob J Hyndman

      1. Yes, inter­ven­tion mod­els will be cov­ered in chap­ter 9. Unfor­tu­nately the R facil­i­ties for fore­cast­ing with inter­ven­tion mod­els are essen­tially non-existent, so I’m going to have to write some code myself. Con­se­quently, the rest of ch9 will be delayed for a few months.

      2. Sorry, but we won’t be cov­er­ing power. The focus of the book is fore­cast­ing, not infer­ence. I don’t know any ref­er­ences on power for inter­ven­tion analy­sis, although I’m sure it comes up a lot when analysing his­tor­i­cal data.

      • New

        Excel­lant, Thanks Rob! I look for­ward to the addi­tions in Chap­ter 9. Many thanks!

      • NEW

        Hi Rob,

        Con­grat­u­la­tions on fin­ish­ing the book! I’ve been check­ing the progress for some time in antic­i­pa­tion of your work on ARIMA inter­ven­tion mod­els. Some time ago (see above) you men­tioned that this would be cov­ered in chap­ter 9. I’ve just had a quick look at the new sec­tions of Chap­ter 9, but don’t find much mate­r­ial related to inter­ven­tion mod­els. I was won­der­ing if you could tell me if I’ve missed these, whether they have been cov­ered else­where, or whether they were cut from this volume?

        • http://robjhyndman.com Rob J Hyndman

          Because of the lack of good R soft­ware for fit­ting inter­ven­tion mod­els, I decided to leave it out for now. I plan to add it when the soft­ware is avail­able. I’m aware of the TSA pack­age, but it is unsuit­able for forecasting.

  • Kon­sta

    Dear authors, in 7/6 (tax­on­omy) in the list below “Some of these meth­ods we have already seen:” in the last row I believe it should read “(A,M_d) = Holt-Winters damped method” instead of “(A,M) = Holt-Winters damped method”, thus the sub­script d is miss­ing. Correct?

    • http://robjhyndman.com Rob J Hyndman

      Now fixed

  • Kon­sta

    In 6/6 in the sen­tence before “Exam­ple 6.3 Elec­tri­cal equip­ment man­u­fac­tur­ing” it is stated “or a non-seasonal ARIMA model (dis­cussed in Chap­ter 7)” but this is dis­cussed in chap­ter 8.

    • http://robjhyndman.com Rob J Hyndman

      Thanks. Now fixed

  • minh nguyen

    When I loaded the pack­age fpp, on the screeen appears the following:

    library(“fpp”)
    Load­ing required pack­age: tseries
    Load­ing required pack­age: quad­prog
    Error: pack­age ‘quad­prog’ could not be loaded
    In addi­tion: Warn­ing mes­sage:
    In library(pkg, character.only = TRUE, logical.return = TRUE, lib.loc = lib.loc) :
    there is no pack­age called ‘quadprog’

    And when I tried the func­tion: seasonplot(tute1[,“Sales”]), this hap­pened: “Error: could not find func­tion “seasonplot” “.

    Do u think there is some­thing wrong with my installation?

    • http://robjhyndman.com Rob J Hyndman

      You have not installed the pack­age depen­den­cies. Please fol­low the instal­la­tion instruc­tions at http://otexts.com/fpp/using-r/

  • Skip

    This looks great so far. I’m on an iPad flip­ping back and forth between web view and “Reader” view. I noticed that in reader view, the for­mu­las at the bot­tom of 1/7 don’t come out in quite the right places in their respec­tive sentences.

  • Stephan Kolassa

    Very nice! One sug­ges­tion: that coef­fi­cients in the log-log (and sim­i­lar) mod­els can be inter­preted as elas­tic­i­ties (sec­tion 4.7) is not com­pletely triv­ial and would make for a nice exer­cise for chap­ter 4.

    • http://robjhyndman.com Rob J Hyndman

      Thanks for the suggestion

  • Stephan Kolassa

    In sec­tion 7.7, a cou­ple of sub­scripts “d” for damp­ened trends are miss­ing, both in the ini­tial part (“Trend = {N,A,A,M,M}”) and in the part where the poten­tially unsta­ble mod­els are listed (“the mod­els that can cause such insta­bil­i­ties are: ETS(M,M,A), ETS(M,M,A)”).

    I couldn’t load table 7.10 on my Android device, but it is fine on my lap­top. May be a glitch on my part.

    And it says “underly” where it should say “under­lie” at the begin­ning of sec­tion 7.7. I am hav­ing a lit­tle harm­less fun in pro­nounc­ing “underly” to rhyme with “orderly” ;-)

    • http://robjhyndman.com Rob J Hyndman

      Thanks the d has been added, and “underly” has been fixed. There is a prob­lem with graph­ics on tablets which we are work­ing on.

  • Stephan Kolassa

    Sec­tion 8.7, Exam­ple 8.2: it says here that “Of these, the ARIMA(3,1,1) has a slightly smaller value.” Sounds to me like “AIC”, “AICc” or “BIC” is miss­ing, depend­ing on what value you are refer­ring to — the con­text does not indi­cate this.

    • http://robjhyndman.com Rob J Hyndman

      Thanks. Now fixed.

  • DP

    Small typo in sec­tion 6/2, in the part about Mov­ing aver­age smooth­ing. Last sen­tence right now is: But if was even, it would no longer by sym­met­ric.
    Maybe it should be: But if was even, it would no longer be symmetric.

    Still read­ing, but so far this book looks really great!

    • http://robjhyndman.com Rob J Hyndman

      That’s odd. The sen­tence is fine but appar­ently you are not see­ing the m. It reads “But if m was even, it would no longer be sym­met­ric.” Do you see the rest of the math­e­mat­i­cal notation?

  • dar­gis

    Hello, do You still work on this book?

  • Yun

    Thanks a lot for the excel­lent text. but I still could not install the library fpp because I am using the lat­est ver­sion of R(2.15). It seems that the library could not be installed in this ver­sion. Could you tell me how I should do for it? Thank you.

    • Floris Padt

      Dear Yun, I am run­ning R ver­sion 2.15.1 (2012–06-22) i386 and do not expe­ri­ence any prob­lems with FPP.

      • Yun

        Dear Floris, thanks a lot for your answers to my ques­tion. After I care­fully check the mes­sage, I found that the R that I was being used is 2.15.0. But the Rcpp library that is needed for fpp is built on R 2.15.1. There­fore I failed to install fpp. I suc­ceeded in installing fpp after I update the R to ver­sion 2.15.1. Thanks a lot for your help.
        Yun

  • efr­ish­man

    This is a won­der­ful book that places empha­sis on both knowl­edge and appli­ca­tion. In review­ing Table 4.1, I believe the slopes for linear-log & log-linear may be swapped.

    • http://robjhyndman.com Rob J Hyndman

      Thanks for spot­ting this. Now fixed.

  • Ibrahim Al-Darrab

    Thank you so much for this won­der­ful book.
    Note: Please give a fig­ure num­ber (Fig­ure 5.14) to the last fig­ure in sec­tion 5/6.

    • http://robjhyndman.com Rob J Hyndman

      Thanks. All fig­ures in that sec­tion are now numbered.

  • Floris Padt

    Excel­lent read­ing, a really small cor­rec­tion can be made in the text of Fig­ure 8.5: Instead of an sub­script there is an under­score in:
    Right: AR(2) with y_t=8+1.3yt-1–0.7yt-2+et.. should be:
    Right: AR(2) with yt=8+1.3yt-1–0.7yt-2+et.

    • http://robjhyndman.com Rob J Hyndman

      Thanks. Now fixed.

  • Andrew Ziem

    On 5/4 the func­tion acf() is cap­i­tal­ized, so the R code given does not exe­cute as is.

    • http://robjhyndman.com Rob J Hyndman

      That is not an error. The Acf() func­tion is part of the fpp package.

  • Patrí­cia Ramos

    Thank you for this excel­lent work Rob and George. I am hav­ing prob­lems in the sec­ond R code of 6/6 sec­tion where you are doing a naive fore­cast of the fit stl object. I get an error in the line fcast <- forecast(fit, method=“naive”) because forecast.stl does not accept the naïve method, only ets or arima. How did you do this plot? Thank you. Best regards, PR

    • http://robjhyndman.com Rob J Hyndman

      The naive option was added in v3.18 in Feb­ru­ary 2012.

  • http://oswco.com dart­dog

    Any way to DL this as a PDF or other? would like to more eas­ily read when not connected?

    • http://robjhyndman.com Rob J Hyndman

      No. It will be avail­able in print once it is fin­ished, and online via this site, but we have no plans to make it avail­able as an elec­tronic download.

  • Jochem

    Great text! I recently had a demon­stra­tion (of com­mer­cial soft­ware) on how a time series with ‘net­work­days’ could improve the fit­ting of a model over a time series and improve the fore­cast. I was hop­ing to find some insights in this text about apply­ing the meth­ods in R. Any inten­tions of extend­ing the text on this at some point?

    • http://robjhyndman.com Rob J Hyndman

      Yes, that’s an exam­ple of the mod­els dis­cussed in Chap­ter 9.

      • Jochem

        OK thanks, I will have a look at it. How­ever, there seems to be some­thing odd with the links on that page. On page http://otexts.com/fpp/9/ the links to sec­tions 9/2 and 9/3 seem to be bro­ken; also they do not appear on the right hand menu. Of course this ‘bug’ might be caused by the fact that those chap­ters aren’t com­pleted yet.

  • Stu­art

    Good book, but I can­not load fpp pack­age and any of the depen­den­cies. R ver­sion 2.15.2. R stu­dio ver­sion 0.97.173, Ubuntu Pre­cise LTS. I can­not install any of the indi­vid­ual pack­ages either. For exam­ple:
    > install.packages(“expsmooth”)Installing package(s) into ‘/home/stuart/R/i686-pc-linux-gnu-library/2.15’
    (as ‘lib’ is unspec­i­fied)
    also installing the depen­dency ‘forecast’

    try­ing URL ‘http://watson.nci.nih.gov/cran_mirror/src/contrib/forecast_4.00.tar.gz’
    Con­tent type ‘application/octet-stream’ length 125516 bytes (122 Kb)
    opened URL
    ==================================================
    down­loaded 122 Kb

    try­ing URL ‘http://watson.nci.nih.gov/cran_mirror/src/contrib/expsmooth_2.02.tar.gz’
    Con­tent type ‘application/octet-stream’ length 245196 bytes (239 Kb)
    opened URL
    ==================================================
    down­loaded 239 Kb

    * installing *source* pack­age ‘fore­cast’ …
    ** pack­age ‘fore­cast’ suc­cess­fully unpacked and MD5 sums checked
    ** libs
    g++ –I/usr/share/R/include –DNDEBUG –I”/home/stuart/R/i686-pc-linux-gnu-library/2.15/Rcpp/include” –I”/home/stuart/R/i686-pc-linux-gnu-library/2.15/RcppArmadillo/include” –fpic –O3 –pipe –g –c calcBATS.cpp –o calcBATS.o
    In file included from calcBATS.cpp:1:0:
    calcBATS.h:36:27: fatal error: RcppArmadillo.h: No such file or direc­tory
    com­pi­la­tion ter­mi­nated.
    make: *** [calcBATS.o] Error 1
    ERROR: com­pi­la­tion failed for pack­age ‘fore­cast’
    * remov­ing ‘/home/stuart/R/i686-pc-linux-gnu-library/2.15/forecast’
    Warn­ing in install.packages :
    instal­la­tion of pack­age ‘fore­cast’ had non-zero exit sta­tus
    ERROR: depen­dency ‘fore­cast’ is not avail­able for pack­age ‘expsmooth’
    * remov­ing ‘/home/stuart/R/i686-pc-linux-gnu-library/2.15/expsmooth’
    Warn­ing in install.packages :
    instal­la­tion of pack­age ‘expsmooth’ had non-zero exit status

    The down­loaded source pack­ages are in
    ‘/tmp/Rtmpzq7eMo/downloaded_packages’

    • http://robjhyndman.com Rob J Hyndman

      I’m using the iden­ti­cal set up and it works for me. Your first error is with the Rcp­pAr­madillo pack­age. Try installing that first.

      • Stu­art

        Thanks, Rob. To get fpp to load I had to delete an empty Rcp­pAr­madillo folder of unknown ori­gin in my R > 2.15 folder and then install Rcp­pAr­madillo. Thanks once again for pro­vid­ing this use­ful software.

  • http://twitter.com/SimaFore BR Desh­pande

    Great book! Look­ing for­ward to the ebook ver­sion.
    BTW not sure if this has been pointed out: there is a minor error in 6/2 Mov­ing Aver­ages. You need a 1/2 in front of the Tt cal­cu­la­tion for the 2x4-MA example.

    • http://robjhyndman.com Rob J Hyndman

      I can’t see any place where there is a 1/2 miss­ing. Can you be more specific?

      • http://twitter.com/SimaFore BR Desh­pande

        Hi Rob,

        “When a 2-MA fol­lows a mov­ing aver­age of even order (such as 4), it is called a “cen­tered mov­ing aver­age of order 4”. This is because the results are now sym­met­ric. To see that this is the case, we can write the –MA as follows:”

        In the equa­tion that fol­lows for Tt, don’t we need a 1/2 which mul­ti­plies the whole expres­sion on the RHS? If not the first equa­tion will sim­plify to

        (yt-2)/4 + (yt-1)/2 + yt/2 + (yt+1)/2 + (yt+2)/4

        instead of the cor­rect form shown in the sec­ond equation.

        • http://robjhyndman.com Rob J Hyndman

          Of course. Thanks. Now fixed.

  • Larry Stone

    Thanks so much for cre­at­ing and main­tain­ing this book — it’s a great help.

    As I was going through the sec­tions I made note of some minor typos and errors, and thought I would pass them along.

    Sec­tion 1–4

    1. The phrase “no. bed­rooms” would prob­a­bly be bet­ter (in a text­book) as “num­ber of bedrooms”.

    2. Dis­cus­sion of Fig­ure 1.1 refers to orange and yel­low sec­tions of the graph, but these sec­tions are instead lighter shades of blue.

    Sec­tion 2–1

    The first sen­tence in the “Scat­ter­plots” overview refers to “The pre­vi­ous two graphs” but there are actu­ally four graphs shown in the pre­vi­ous section.

    Sec­tion 2–2

    In the first bul­let point after the auto­cor­re­la­tion graph, you say “the troughs tend to be two quar­ters apart”. The troughs tend to be four quar­ters apart, but two quar­ters off­set from the peaks (which is the point made in your sec­ond bullet).

    Sec­tion 2–5

    In the sub­sec­tion titled “Train­ing and test sets”, you state that you “pre­fer to use ‘train­ing set’ and ‘test set’ in this book”. How­ever, in the ear­lier sub­sec­tion titled “Scaled errors” you use the term “in-sample” (ital­i­cized) rather than “train­ing set”.

    Sec­tion 4–4

    This also uses “out-of-sample” and “in-sample” rather than “train­ing” and “test”.

    Sec­tion 5–2

    The “R Out­put” sec­tion in the Aus­tralian quar­terly beer pro­duc­tion sec­tion starts out closed, but from the way the text flows it should prob­a­bly start out opened. Click­ing to open it is not a big deal, but the read­ing would flow bet­ter if it were ini­tially open.

    Fig­ure 5–7 refers to orange and yel­low regions when these are now shades of blue, as for Fig­ure 1.1.

    I’m start­ing to dig into sec­tion 6 now, but thought I’d post these before I lost track of them. Thanks again for all your hard work and insight.

    • http://robjhyndman.com Rob J Hyndman

      Thanks. Very help­ful. I’ll get these fixed.

  • PRamos

    Hi Rob and
    George! Con­grat­u­la­tions for your excel­lent book!

    I think there is
    some­thing wrong with Exam­ple 8.3 because the R code tsdisplay(diff(euretail,4))
    does not match with Fig­ure 8.15 and the same hap­pens with Fig­ure 8.16 (R code tsdisplay(diff(diff(euretail,4)))).
    Could you please see what is wrong?

    Thank you!

    • http://robjhyndman.com Rob J Hyndman

      Thanks for spot­ting the error. Now fixed. You might have to clear your cache to see the update.

  • Eka­te­rina

    Hi Rob and Geogre!

    First of all thank you for very help­ful book.

    I have a lit­tle com­ment on chap­ter 5/5.

    It seems to me that vec­tor beta should be as (b0, b1, …, bk)’, Now there is no beta_0. And we mul­ti­ply nx(k+1) matrix with kx1 vector…

    Kind regards,

    Katia

    • http://robjhyndman.com Rob J Hyndman

      Thanks. I’ll fix it.

  • http://twitter.com/FlorisPadt Floris Padt

    Dear Rob and George,

    Could it be that the for­mula of fig­ure 8.5 AR(1) doesn’t match the figure?

    I expected the con­stant to be around 18 instead of 2, so
    par. 8/3 Autore­gres­sive Mod­els, Fig­ure 8.5:
    AR(1) with yt=2–0.8yt-1+et. -> yt=18–0.8yt-1+et.

    Same seems to apply for:
    par. 8/4 Mov­ing Aver­age Mod­els, Fig­ure 8.6:
    MA(1) yt=20+et+0.8et-1. -> yt=5+et+0.8et-1.

    • http://robjhyndman.com Rob J Hyndman

      Well spot­ted. I’ll fix the graphs.

  • smpires

    Hi Rob and George.

    First i would like to thank you for this very help­ful book.

    I started to read the book and i am look­ing for­ward to read chap­ter 10, so i would like to know if pos­si­ble, when is it expected to be released.

    thank you.

    • http://robjhyndman.com Rob J Hyndman

      We plan to have a com­plete ver­sion avail­able in Feb­ru­ary, both online and in print via Amazon.

  • Brian

    Very nice work so far. One sug­ges­tion — that has trou­bled me per­son­ally is when cre­at­ing an econo­met­ric model using time series data (time series data and pre­dic­tors) is when to use lin­ear regres­sion (say with robust stan­dard errors for ser­ial cor­re­la­tion) and when to use Arima with pre­dic­tors. Is the lat­ter less efficient?

    • http://robjhyndman.com Rob J Hyndman

      If there is ser­ial cor­re­la­tion, then regres­sion with ARMA errors is the way to go. It is more effi­cient, not less.

  • http://www.facebook.com/austin.d.trombley Austin D. Trombley

    Warn­ing mes­sage:
    pack­age ‘fpp ’ is not avail­able (for R ver­sion 2.15.2)

    Any idea how to fix this?

    • http://robjhyndman.com Rob J Hyndman

      Try another CRAN mir­ror. I am using it on Rv2.15.2.

  • Car­los

    I would like use your online book as text­book in my course of fore­cast­ing tech­niques in an span­ish uni­ver­sity. could you give me a date when the whole text will be avail­able online? Thanks a lot!

    • http://robjhyndman.com Rob J Hyndman

      Before the end of Feb­ru­ary. It is almost fin­ished (although some parts have yet to be uploaded to the web site).

      • Car­los

        Thanks!

  • Osman

    Dear Prof. Hyndman

    I guess it was small typo in R code on page: http://otexts.com/fpp/8/5/
    below fig­ure 8.7.

    Either it should have been max.Q=3 in below func­tion or it should be ARIMA(0,0,0) in next below line.

    > fit <- auto.arima(usconsumption[,1],max.P=0,max.Q=0,D=0)

    ARIMA(0,0,3) with non-zero mean
    Coef­fi­cients:
    ma1 ma2 ma3 inter­cept
    0.2542 0.2260 0.2695 0.7562
    s.e. 0.0767 0.0779 0.0692 0.0844

    • http://robjhyndman.com Rob J Hyndman

      No, that’s fine. max.Q con­trols the sea­sonal MA order, whereas the 3 in the cho­sen model is the non-seasonal MA order.

  • Deep­ankar

    thank you. As an MBA stu­dent this is a great resource.

  • Katia

    Hi Rob and George!
    As many oth­ers I also wait for com­ple­tion of the book. Espe­cially Chap­ter 10 :)
    When it will be ready? Ear­lier Feb-March was men­tioned.…
    Thank you very much for this use­ful infor­ma­tive book. It helps a lot in under­stand­ing back stages of mod­els avail­able in SAP APO DP and let me to choose them cor­rectly
    Kind regards,
    Katia

    • http://robjhyndman.com Rob J Hyndman

      Hi Katia. The book is fin­ished, but we have had a delay in upload­ing the final ver­sion to this web­site. Hope­fully in the next week or two.

  • Erik P.

    Small edi­to­r­ial com­ment: In sec­tion 3/4, the phrase “estimate-talk-estimate” has a trail­ing, but not a lead­ing dou­ble quote.

    • http://robjhyndman.com Rob J Hyndman

      Thanks. Now fixed

  • Erik P.

    At the begin­ning of sec­tion sec­tion 4/8, you say the regres­sion line plot­ted is C-hat = 0.52 + 0.32 I, where C is the per­cent­age change in real per­sonal con­sump­tion expen­di­ture and I is the per­cent­age change in real per­sonal dis­pos­able income. You con­clude that a 1% increase in per­sonal dis­pos­able income will result in an aver­age increase of 0.32% in per­sonal con­sump­tion expen­di­ture. I think this should be phrased as: a 1% *higher* increase in per­sonal dis­pos­able income will result, on aver­age, in a 0.32% *higher* inclrease in per­sonal con­sump­tion expen­di­ture — or alter­na­tively, a 1% increase in per­sonal dis­pos­able income will result in an aver­age increase of 0.84% in per­sonal con­sump­tion expenditure.

    • http://robjhyndman.com Rob J Hyndman

      Thanks. Now fixed.

  • Erik P.

    The cap­tion of Fig­ure 5.7 talks about orange and yel­low regions, whereas the graph has these regions in dark and light grey.

  • bob

    Do you con­sider to pub­lish it in a ebook-friendly file format?

    • http://robjhyndman.com Rob J Hyndman

      Pos­si­bly. Our next pri­or­ity is to put out a print ver­sion. We may con­sider it after that. Unfor­tu­nately, the kin­dle plat­form seems too lim­ited to han­dle math­e­mat­i­cal equa­tions effectively.

  • Neerav Shah

    Great work! Thanks a ton!

  • Barry Quinn

    Rob and George, thanks a mil­lion for cre­at­ing this superb resource.

    I have been using it on my under­grad­u­ate finan­cial econo­met­rics course this year and hope to inte­grate more of it in the com­ing years.

    Specif­i­cally I have cre­ated some resources using chap­ter 2 and 6 but unfor­tu­nately my course has been based on Stata up to now so i am not sure if it would be worth shar­ing them with you and this com­mu­nity ? (I hope to change to R going forward)

    Any­way a fan­tas­tic resource and i will be donat­ing gen­er­ously to your cause at the end of the semester.

    • http://robjhyndman.com Rob J Hyndman

      Hi Barry. Other peo­ple might be inter­ested. If you email them to me (Rob.Hyndman@monash.edu), I can add them to the resources page.

  • David

    Thank you for this quite use­ful book. I would sug­gest adding a fourth cat­e­gory to the intended audi­ence or oth­er­wise sug­gest­ing that there are a broad range of con­texts in which these meth­ods would be use­ful — it seems that it is the exam­ples, but not the sta­tis­tics, are business-specific.

  • Xavier

    Hi and thank you for this online book, very clear and pre­cise.
    I have a ques­tion regard­ing the fore­cast­ing method using decom­po­si­tion. You give an exam­ple using stl. How­ever, you don’t dis­cuss the even­tual bound­ary effects that may affect the decom­po­si­tion in this sit­u­a­tion. In my expe­ri­ence, the boudary effects in stl are rel­a­tively impor­tant. Do you have guidelines/recommendations to avoid these bound­ary effects? Thanks

    • http://robjhyndman.com Rob J Hyndman

      I’ve never seen any seri­ous bound­ary effects with stl. The under­ly­ing trend esti­mate uses local lin­ear regres­sion by default, so unless there is strong cur­va­ture near the end, the bound­ary bias will be small.

  • Isaac

    In exam­ple 6.3 (in sec­tion 6.6) I think you mean to use ylab instead of xlab for “New orders index”

    • http://robjhyndman.com Rob J Hyndman

      Thanks. Now fixed, although you won’t see the new fig­ure unless you clear your cache.

  • Indranil

    This is a very help­ful book! You guys have done a great job.

    Sug­ges­tion — In the chap­ter cov­er­ing Holt-Winters, in table 7.6 (mul­ti­plica­tive Holt Win­ters) the cal­cu­la­tion of y(hat) is not very clear (till Dec 10). It would be great if you could explain that in some more detail. Thanks!

  • Brian

    Fan­tas­tic! Is there any way to see all the pages and print them for eas­ier reading?

    • http://robjhyndman.com/ Rob J Hyndman

      There will be a print ver­sion avail­able in a few months.

  • Jan Göpfert

    In chap­ter 6/3 Clas­si­cal decom­po­si­tion under Addi­tive decom­po­si­tion Step 3, the word­ing can be mis­lead­ing (I was mis­led…). Some­thing like the fol­low­ing might be clearer:

    “To esti­mate the sea­sonal com­po­nent, do the fol­low­ing: for each month, sim­ply aver­age the detrended val­ues for that month. […]”

    Also, an optional expla­na­tion using mod­ulo might make things clearer for some:

    hat{S}_t = tilde{S}_{t mod 12}

    Thanks for the awe­some book.

  • Tari­garma

    Thank you for mak­ing this book avail­able on the inter­net, cur­rently it is one of my bibles since I am using it as a ref­er­ence for my thesis.

    Just men­tion­ing, is there some kind of error in the chap­ter 7/1, the equa­tions seem to be in the LateX nota­tion, or I dont know if it is my browser (Firefox).

    • http://robjhyndman.com/ Rob J Hyndman

      Try refresh­ing the page.

  • Eva Yamila Catela

    I would like to thank you, Rob and George for FPP and the online book Forecasting…I tried to repli­cate the exam­ples of fore­cast­ing hier­ar­quical or grouped time series (Sec­tion 9.4) but could not because the objects “bts” and “vn” are not avail­able in fpp or hts. How can I obtain this objects? I need to see the data struc­ture.
    Many thanks for this, it’s a great resource!

    • http://robjhyndman.com/ Rob J Hyndman

      vn is part of the fpp pack­age v0.5. Make sure you have the lat­est version.

      bts was just an exam­ple, and was not intended to be replicated.

  • David For­rest

    It might be nice to add the “Pref­ace” and the “Using R”, etc., from the top tabs to the table of con­tents and make sure they are in the book. In my read­ing of it, I started in the mid­dle and devel­oped tun­nel vision on using the table of con­tents for nav­i­ga­tion. After fail­ing to find what I needed in the TOC, I searched through these com­ments here before I saw a post on installing ‘fpp’

    I’d guess that the printed book will have an index and some appen­dices for these, but it might be nice to have them in the elec­tronic book as well. A link to http://cran.r-project.org/web/packages/fpp/fpp.pdf or the live index you get from ?fpp/Index might be nice as well.

    Regard­less of whether or not you use my feed­back, I like the book, and will buy it to sup­port your work.

    • http://robjhyndman.com/ Rob J Hyndman

      Thanks for the sug­ges­tions. We are redesign­ing the site in the next few weeks, so look out for some changes.

  • Isaac

    This is a won­der­ful resource. Thank you so much for putting it together. As a novice to fore­cast­ing, it would be help­ful to have a sec­tion on when to use the var­i­ous meth­ods described in the book. In other words, in what sit­u­a­tions is it best to use lin­ear regres­sion vs ran­dom forests vs ARIMA, etc.? What are the pros and cons of each.

    • http://robjhyndman.com/ Rob J Hyndman

      Thanks for the suggestion.

  • yun

    Thank you for the great work. I found that the results for cal­cu­lat­ing lev­els at alpha=0.6 for 7/1 are dif­fer­ent to what appear in the text book. The results that I cal­cu­lated with excel are

    446.7

    446.7

    451.4

    454.0

    435.7

    448.1

    443.6

    432.6

    464.1

    489.2

    511.8

    513.3

    501.8

    for the period t from 0 to 12. The other results for alpha = 0.2 and the opti­mal alpha=0.89 and level_0 are all the same to those in the text­book. The results for alpha=0.6 in the text­book are

    446.7

    446.7

    450.6

    453.1

    438.4

    447.3

    444

    434.6

    459.9

    483

    504.9

    509.6

    501.9

    The dif­fer­ence is start from t=2. Am I wrong in the calculation?

    • http://robjhyndman.com/ Rob J Hyndman

      Thanks. You are cor­rect. I had fixed this on my local copy but for­got to update the web­site. The num­bers you give are not quite cor­rect, prob­a­bly due to round­ing error. The val­ues now on the 7/1 page are based on the orig­i­nal data, not the rounded data shown in the table.

      • yun

        Thanks for your quickly respond­ing. The data for alpha=06 seems updated now. But there is still a mis­print for the last level in 2007. It should be 501.8 not 513.3. Besides, I don’t know how to obtain the orig­i­nal data with­out rounded and I have to use the data as you have pro­vided in rounded. Would you tell me how to get the data appeared in your text­book? I think these data may be in fpp library but I don’t know how to access these data. I appre­ci­ate your advice.

        • http://robjhyndman.com/ Rob J Hyndman

          Thanks again. The orig­i­nal data are in the oil object within the fpp pack­age on R.

          • yun

            Thanks a lot. I have found the doc­u­ment of the fpp package.

  • Erik P.

    The cap­tion for fig­ure 7.10 (sec­tion 7/7) reads: “Fore­cast­ing inter­na­tional vis­i­tor nights in Aus­tralia from an ETS(M,Ad,M) model”. Accord­ing to the text and the other fig­ures, that should be ETS(M, Md, M).

    • http://robjhyndman.com/ Rob J Hyndman

      Thanks. Now fixed.

  • Erik P.

    In table 7.9 (sec­tion 7/6), the left col­umn con­tains dupli­cate entries; I think every instance of (X, Y) (X, Y) is meant to be (X, Y) (Xd, Y).

    • http://robjhyndman.com/ Rob J Hyndman

      Thanks. Fixed.