Hamilton Time Series

[Toney Talbot]

NOTE: I have read the topic re "books for self-studying time series analysis," this question is intended to be different in a very specific way, and I am looking for answers that would not be relevant to that topic's OP).

I very much like Hamilton's Time Series Analysis book in terms of both the breadth of coverage and the depth (i.e., not too shallow not too deep relative to my personal taste and training). Also, I am in the economics / investment management field so I like the slant on economic topics. What I DON'T like is that it's not available on e-book - a lot of my reading time is while commuting, etc, and it's hard to haul around a book that's bulkier than my laptop. I have inquired and there seems to be no intention of bringing it out on Kindle / Google Books / etc.

So, my question is: Can someone here who is familiar with Hamilton and "similar" texts recommend something that has similar depth and scope, but is available on Kindle or Google Books (and if it's on Kindle, with the additional requirement that the equations actually render properly). Of course being written less than 21 years ago might also help, but I'll settle for older books all things being equal.

I recommend Time Series Analysis and Its Applications: With R Examples. It's not from econometrics perspective though. The plus is that it comes with R package called astsa, which is a great piece of software in itself.

Professionally I am analysing high-frequency data coming from motion sensors and alike.I would like to "up my theoretical background game" in this area and am therefore looking for recommendations to books about (I guess) statistics and probability theory concerning time series pehomena.

Hamilton "Time Series" -LinkIt is a LONG book (816 pages) but actually does not cover THAT much material. However, instead it is very user-friendly which provides a lot of details for the material it covers. It is a standard reference in Economics PhD classes for Time Series (which are important topics for macroeconomists).

Brockwell "Time Series: Theory and Methods" Link - This used to be (still is?) the main reference for Time Series back in the day for those theoretically inclined. Heavy on mathematics, so only for people with strong mathematics/statistics background.

I have found there are several "schools of thought" in the field that pervade theory, notation, and approach to essentially the same methods: control (ODEs), statistics (ARIMA methods), signal theory (Kalman filters)...

Using the same convention as in Hastie, Friedman, and Tibshirani (2001), the symbol ? indicates a technically difficult section which may be skipped without interrupting the flow of the discussion.

This is not the first (or the last) book that has been written on time series analysis. Indeed, this can be seen as a book that brings together and reorganizes information and material from other sources structuring and tailoring it to a course in basic time series analysis. The main and excellent references (which are far from being an exhaustive review of literature) that can be used to have a more in-depth view of different aspects treated in this book are Cochrane (2005), Hamilton (1994) and Shumway and Stoffer (2010).

The authors are particularly grateful to James Balamuta who introduced them to the use of the different tools provided by the RStudio environment and greatly contributed to an earlier version of this book:

Many books on the subject fall into two categories: classic texts with the basic theories and fundamentals of time series analysis, and revised editions of academic textbooks with real-world examples and exercises. We picked an array that covers the initial introduction to references and guides along with your time series analysis self-study.

This book is a basic introduction to time series and the open-source software R, and is intended for readers who have little to no R knowledge. It gives step-by-step instructions for getting started with time series analysis and how to use R to make it all happen. Each module features practical applications and data to test the analysis. The co-author Paul Cowpertwait also features the data sets on a companion website.

The book gives a good overview of time series analysis without being overwhelming. It covers the basics, including methods, forecasting models, systems, and ARIMA probability models that include studying seasonality. It also includes examples and practical advice and comes with a free online appendix.

Time series analysis is a complex subject, and even these books barely scratch the surface of its uses and evolution. In order to utilize the analysis to its fullest, you have to stay current with new trends and theories, as well as continue to deepen your understanding. To learn more about theories and read real customer stories, check out our time series analysis resources page.

The hfilter function applies the Hamilton filter to separate one or more time series into additive trend and cyclical components. hfilter optionally plots the series and trend component, with cycles removed.

[TTbl,CTbl] = hfilter(Tbl) returns tables or timetables containing variables for the trend and cyclical components from applying the Hamilton filter to each variable in an input table or timetable. To select different variables to filter, use the DataVariables name-value argument.

[___] = hfilter(___,Name=Value) specifies options using one or more name-value arguments in addition to any of the input argument combinations in previous syntaxes. hfilter returns the output argument combination for the corresponding input arguments. For example, hfilter(Tbl,LeadLength=4,DataVariables=1:5) applies the Hamilton filter to the first five variables in the input table Tbl, and, for each selected variable, specifies the lead yt + 4 as the response variable in the filter weight regression.

[___,h]= hfilter(___) plots the specified series and their trend components, and additionally returns handles to plotted graphics objects. Use elements of h to modify properties of the plot after you create it.

trend and cyclical are 235-by-1 vectors containing the trend and cyclical components, respectively, resulting from applying the Hamilton filter to the series with default lead and lag lengths. The first 7 values are NaNs.

Load the Schwert stock data set Data_SchwertStock.mat, which contains monthly returns of the NYSE index from 1871 through 2008 in DataTimeTableMth, among three other variables (for details, enter Description). Remove all missing observations from all series.

TQTT and CQTT are 220-by-4 timetables containing the trend and cyclical components, respectively, of the series in TTQ. Variables in the input and output timetables correspond. By default, hfilter filters all variables in the input table or timetable. To select a subset of variables, set the DataVariables option.

Because the data is disaggregated, the outputs of the daily data have more rows than from the quarterly data. The filter results of the daily inputs are equal among the corresponding outputs, but hfilter returns tables of results, instead of timetables, when you supply data in a table.

Filter weight regression response variable lead h, in units of data periodicity, specified as a positive integer or vector of positive integers. That is, the response variable in the regression is yt+h.

Variables in Tbl that hfilter filters, specified as a string vector or cell vector of character vectors containing variable names in Tbl.Properties.VariableNames, or an integer or logical vector representing the indices of names. The selected variables must be numeric.

Regarding a setting for the LeadLength name-value argument, Hamilton [2] states "If we are interested in business cycles, a 2-year horizon should be the standard benchmark." Regarding a setting for the LagLength name-value argument, the article states "One might be tempted to use a richer model to forecast yt+h, such as using more than 4 lags, or even a nonlinear relation. However, such refinements are completely unnecessary for the goal of extracting a stationary (cyclical) component, and have the significant drawback that the more parameters we try to estimate by regression, the more the small-sample results are likely to differ from the asymptotic predictions."

3a8082e126