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For the four-hour exam, Thursday June 2, I remind you that this is a no-book exam, but that each student can bring *one page of handwritten notes*. 

I've been asked to say something about "the form" of the four-hour exam, and don't have a very precise answer to that. But here is my last four-hour exam set (for a different course!), autumn 2021. So, to a vague approximation, this is how Nils's four-hour exam sets might look like: 

/studier/emner/matnat/math/STK4021/h21/exam_stk4021_2021.pdf 

No teaching on Kristi Himmelfartsdag (but listen to BWV 11). We therefore have a round of Questions & Answers on Friday 27th, from 13:15 to about 15:00. This takes place in Room 819, eighth floor of Abel.

Exam preparations? Well, go through the Nils Collection of Exercises and Lecture Notes, and guess away. Also, read & study the curriculum. 

As explained last week I'm busy with the STABILITY AND CHANGE workshop at Prio Wed-Thu May 11-12 (see separate information for this; there will be a few time series on peace-and-conflict, democracy parameters, etc.). 

We meet Thursday 19th, with exercises, exam preparations, "repetering", looking back at the earlier parts of the curriculum, etc. If we wish to, we might have one more meeting, during the final week of May. For Thu 19th, do these exercises: Exams May 2018, no. 1; June 2016, no. 3; May 2014, no. 1. Then Nils Collection Exercises 31, 32, 33, 35.

I will have a *final version* of the Nils Collection of Exercises and Lecture Notes within a few days, with just a bit on the Kalman Filter from Ch 6. Otherwise we spend time consolidating our knowledge, for the exam.

Thanks for your efforts with the Oblig (delivered Tue 3rd). I'll manage to go through them all in the course of today (Wed 4th), and will then use *part of the time* tomorrow, Thu 5th, to go through the Oblig material.

In addition, we start out on the state space models, Sections 6.1, 6.2, 6.3, the last part of our curriculum.  

I've uploaded yet another new version of Exerises and Lecture Notes, version H, with so far 35 exercises, dater 30 Aprill 

For Thu May 5, I use a bit of time to round off more from Ch 4, and start on Sections 6.1, 6.2, 6.3, the last part of the curriculum, with state-space models. 

Work with these exercises: Exams May 2018, no. 1; June 2016, no. 3; May 2014, no. 1. Then Nils Collection Exercises 31, 32, 33, 35.

Thanks for pointing out this small detail today, dear students, for the OBLIG, Exercise 1: 

In point (g) I've written "Do this with your simulated data from point (c)", but as is somewhat clear from the context I meant "Do this with your simulated data from point (d)". 

I apologise for being late with this particular message. But Version G of the Nils Collecction is now on the website (30 exercises, 29 pages, as of April 26). For Thu April 28, we'll be rounding off all material from Ch 4, including the Whittle log-likelihood and its uses, and certain aspects of the periodogramme, estimation of the spectral density, etc.

I will also spend *some* time on Exercises 28, 29, about using the Whittle for MA(q) and AR(p), and *some* time on a few earlier Exam Set questions (which you find on the website): May 2018, no. 1; June 2016, no. 3; May 2014, no. 1.

Otherwise continue work on the Oblig!, with deadline Tue May 3.

The Oblig exercise is now out, Tue April 19. It has three exercises, and the pdf also has a generic information page plus a brief appendix with just a few R things. There's a dataset to work with, given here at the course website as "beerdata"; the Oblig appendix explains how you can read these data into your computer.

The deadline for submitting your report, as a single pdf to the Canvas system, is Tue May 3, at 13:58. (I've incorrectly written "Tuesday May 2" in the Oblig pdf, but it should by all means ve Tue May 3.)

For Thursday this week, we go through more from Sections 4.2 and 4.3, with periodogram, the Discrete Fourier Transform and its inverse, leading also up to the Whittle log-likelihood. We've then been through 75 percecnt of all from Ch 4. 

Curriculum list for our course is as follows. The main material is from the Shumway and Stuffer book, Time Series and Its Applications, 4th ed., 2016; also, all exercises that we've been through in class, from Nils Lid Hjort's Exercises and Leture Notes collection, are defined as part of the curriculum. That same remark applies to The Oblig, the obligatory exercise set that we have just after Easter. 

From the S & S book: 

Ch. 1: sections 1, 2, 3, 4, 5; 6 is kursorisk pensum.

Ch 2: sections 1, 2; 3 is kursorisk pensum.

Ch 3: sections 1, 2, 3, 4, 5, 8.

Ch 4: sections 1, 2, 3, 4, 5.

Ch 6: sections 1, 2, 3.

"Kursorisk pensum", cursory curriculum, means that one should read through these approprriate parts, and "know what goes on", but this is not seen as part of the active part of curriculum.

The four-hour written exam in June is a no-book exam, but each candidate can br...

We have started in Ch 4, the spectral domain, etc., and after a little while we will return to a few issues to round off Ch 3. This concerns in particular the so-called Whittle likelihood for stationary Gaussian time series, and using that tool we will learn a bit more also regarding estimation of parameters in the AR(p), MA(q), ARMA(p,q) models.

For Thu April 7, we will work more with Sections 4.1, 4.2, 4.3 in the book, including the periodogram, spectral densities, etc.

For Thu April 7, work with Nils Collection Exercises (Version F, as of March 24), 17, 21, 22, 23. Also, complement Exercise 17, by simulating a time series from an MA(2) model, and carry out ML estimation, using the x = A w reprtesentation from my lecture March 31.

I will write out more details for the next update of the Nils Collection, and there will me further R scripts.

I've uploaded "version F", so far 23 pages, as of 24.iii.22, of the Nils Exercises and Lecture Notes. When we've been through Exercises 19, 20, 21, 22, 23, we have somehow also been through more than 51 percent of Ch 4.

For Thu Mar 31, I will essentially go through first Exercise 17 (with comments!), then these 19, 20, 21, 22, 23 (with comments!). Work with all of these, and Exercise 22, about midnight stargazing a hundred years ago, is a good illustration of an important class of time series models, and their interpretation and analysis.

Note com11c, a script for estimating parameters in an MA(3); this can easily be generalised to any MA(q).

I have very soon had my "four symptom free days", ending my modest covid experience. But I do follow the FHI and UiO rules, and according to these I should not teach Thu Mar 24. I've tried to find a vikar, a substitute, without succeeding. 

By tonight or tomorrow I will have uploaded an extended version of the Exercises and Lecture Notes, with new exercises, partly starting Ch 4. I'll also post a precise curriculum list, from which one sees that Ch 4 is so to speak from the 0.70 to the 0.90 of the full 0.00 to  0.99 of the course. 

I will also upload a few more R scripts, relating (a) to estimation in AR(p), MA(q), ARMA(p,q) models and (b) initial frequency domain methods.

I'm sorry to report, and rather late, the evening before, that I've fallen ill -- and let me be brave enough and specific enough to tell you I've had a positive covid test. I'm just moderately ill, no bothersome symptoms, and it feels like having a somewhat unusual winter cold. Though I'm up and about, and able to work, I do follow the UiO and Math Dept rules, and stay at home, in splendid isolation, for a few days.

Within a few days I'll upload an extended Nils Collection of Exercises and Lecture Notes, with emphasis on (a) estimation in AR(p), MA(q), ARMA(p,q); (b) gentle start on Ch 4, frequency domain modelling, analysis, applications. So please start reading the first two sections there. Ch 4 is our last "major weightlifting" for the course. 

We will also soon start doing *earlier exam set questions*, which you find at the course website; these are from 2010, 2012, 2016, 2018, apparently. 

More information soon. 

An extended version D is not on the website, "version D", with 18 pages, dated 9/iii/22. There will be more, with ARMA(p,q), and some exercises for a couple of real datasets, soon.

The book is good!, but the AR(p) material, in particular, is somehow spread through the long Ch 3. My Exercises 15 and 16 are meant to summarisethe essentials for these time series models, with the key steps from motivation, to definition, to representation, to the polynomials associated with the bachshift operator, to the key equations, to the estimators, and more.

1. We spent time going through the New Haven annual temperatures dataset, and I've uploaded the R script "com14b" to the course site. We also travelled through the basics of the AR(p), with polynomials associated with the \phi and \psi representations, how to estimate the \phi parameters, etc.

2. I need a couple of days to write up some AR(p) and MA(q) and ARMA(p,q) exercises and lecture notes; soon enough there will be an updated version of the Nils Collection.

3. More details will be put up here, pretty soon, regarding exercises. Some of these are as follows: simulate, estimate, from these important time series models: AR(p), MA(q), ARMA(p,q). Keep p and q moderately low, like 2. In addition, I'll find a real dataset for us to work with, exhiting AR(p) in action.

4. Next week more on MA(q) and ARMA(p,q), from Ch 3 of the book.

1. On Thu Feb 24 we spent time discussing general issues for prediction and prediction uncertainty, the general multinormal model, and Nils Exercises 9, 10, 11, 12, 13. We also started Ch 3, and will spend working time getting familiar with AR(p), MA(q), ARMA(p,q). So far our favourite serious model example have been versions of AR(1).

2. For Thu Mar 3, work with these. (i) In R, find the dataset called "nhtemp", annual temperatures at New Haven, from 1912 to 1971. Translate to Celcius!, then try a couple of models, including linear regression plus autocorrelation. Check whether the autocorrelation is significantly present. Give an estimate and 90 percent prediction interval for the NH temperature in 1972. (ii) Simulate n = 200 data points x_t from an AR(2) model with parameters (0.33,0.22), then try to estimate these values from your simulated data. Repeat the experiment say 100 times. (iii) Similarly simulate n = 200 data points from the MA(2) model, with parame...

1. Dates for the OBLIG will be finalised within a few days, but the tentative dates are t_0 = Tue Apr 19, the day after Easter, to t_1 = Tue May 2. Details will follow.

2. We've rounded off Ch 2, and read to really start on hard-core time series models in Ch 3, from next week.

3. I've uploaded so far com1d, com101a, com5a, com6a; check these carefully, so that you know you can construct similar or extended versions when needed.

4. I've also uploaded Version C of the Nils Notes (so far, 13 exercises, 13 pages). For Thu Feb 24: do the rest of Nils 9 (see my code com6a); construct an estimate and a 90 percent confidence interval for the number of skiing days in 2016, based on all data up to 2015; then do Nils Exercises 12, 13.

1. On Thu Feb 10 we dealt with the first half of Ch 2, and with an extended discussion of AIC and BIC. We also went through modelling, model fitting, and analysis, of the JJ dataset and the chicken dataset. The AIC and BIC model selection schemes are more general than in the book; see Nils Notes Exercises 9, 10, in particular.

2. I've placed R scripts com1d and com101a on the website, with more to come, soon. I'm also uploading Nils Exercises and Lectures Notes Version B there, now 12 pages.

3. For Thu Feb 17, work (hard) with Nils Exercise 11, the skiing days at Bj?rnholt. How many skiing days will there be in 2013 (given everything observed and counted up to 2012)? Also do Nils Exercises 8, 9, 10.

4. Next week we are close to rounding off Ch 2, with relatively speaking more time needed for the models and methods of Ch 3 after that. There will more technical information here reasonably soon.

1. Note that the Nils Collection of Exercises and Lecture Notes are placed here at the course website. The first version has 6 pages, and there will soon be more.

2. On Thu 3 we did the exercises listed, from Ch 1, and also discussed in some gerenality the theory and practical algorithmic application of the Grand Theorem for parametric models: the ML estimator is approximately normal and unbiased, with covariance matrix approximately equal to the inverse observed Fisher information matrix. See the com1d script for an illustration, with the JJ data.

3. We rounded off Ch 1 and started Ch 2.

4. Exercises for Thu Feb 10: First, do the JJ dataset, playing with one or two more models, using perhaps the com1d as the starting point. Then, do Nils Exercises 5, 6. Then, model and analyse the *chicken* dataset of the book (available in the astsa package), using "linear regression plus correlated error terms", and attempt the differencing operator. For...

There are still things going on after the fire trouble in VB last week, so Aud 4 cannot be used this week. So we're in  *room 723*, 7th floor Abel, on this particular Thursday, 3 Feb.

I will have the first start version of "Exercises and Lecture Notes" on the webpage by Wednesday, 2 Feb.

1. On Thu Jan 27, in a somewhat dark Aud. 4 due to the fire in the herretoalettomr?de three days earlier, we went through these exercises: 1.4, 1.6, 1.20; proving formula (1.35), with implications for the case of \rho(h) = \rho^j; initial regression modelling attempts for the JJ dataset.

2. We then discussed central concepts and methods from Ch 1, with emphasis on the covariance function \gamma(h) and correlation function \rho(h), and their empirical counterparts, the important acf(xdata) algorith. In particular, theory was given to explain what happens with the acf in the case of i.i.d. data.

3. I'm placing my R script com1d on the website, with regression things for the JJ dataset. Run its different parts, make sure you understand what they accomplish, and play with variations.

4. For Thu Feb 3, first try out a couple of more regression models for the JJ dataset, perhaps taking my com1d as point of departure. Include a cyclic term for the...

1. We've started the course! On Thu Jan 20 I gave a broad introduction to the various time series themes we'll be working with, via key concepts and indication of models and methods; lots of detail will come in the coming few weeks.

2. We'll be needing the first three weeks of the course to go through be basics of Ch 1, with various footnotes and excursions.   

3. We'll be using the R package "astsa", so please jump into it, get familiar with its basic setup, read the vignette, have a look at a few datasets. In particular, check the dataset "jj" (Figure 1.1 in the book), try a few simple models, to see what goes on. In particular, try simple linear regression, and check residuals; identify in which ways that approach will not be good enough.

4. Prove formula (1.35) in the book, in detail, and apply it to the case where the correlation function is rho(h) = rho^h, with rho inside (-1,1).

5. Simulate a time seri...

1. We've started the course! On Thu Jan 20 I gave a broad introduction to the various time series themes we'll be working with, via key concepts and indication of models and methods; lots of detail will come in the coming few weeks.

2. We'll be needing the first three weeks of the course to go through be basics of Ch 1, with various footnotes and excursions.   

3. We'll be using the R package "astsa", so please jump into it, get familiar with its basic setup, read the vignette, have a look at a few datasets. In particular, check the dataset "jj" (Figure 1.1 in the book), try a few simple models, to see what goes on. In particular, try simple linear regression, and check residuals; identify in which ways that approach will not be good enough.

4. Prove formula (1.35) in the book, in detail, and apply it to the case where the correlation function is rho(h) = rho^h, with rho inside (-1,1).

5. Simulate a time seri...

In view of the recent developments and practical guidelines related to the covid-19 (and the delta and the omicron), teaching will indeed be by "physical presence", i.e. in Auditorium 4, as planned, Thursdays 9-12, and not by zoom. We are advised to use the 1-meter-distance rules, though. 

I will post certain notes and explanations and roadmaps, as the course progresses, along with exercises and so on.

We'll soon enough know the consequences of the New Tentative Rules, as of 13/i, but it appears likely that we can "behave as ususal", with teaching at campus -- not too many in the same room, and with 1-alen distance. It'll be good for us all to not to be forced into zoomology.

https://www.vg.no/nyheter/innenriks/i/qWXKBe/slik-blir-corona-hverdagen-for-unge