Endogenously Detecting Structural Breaks in a Time Series: Implementation in R

The most conventional approach to determine structural breaks in longitudinal data seems to be the Chow Test.

From Wikipedia,

The Chow test, proposed by econometrician Gregory Chow in 1960, is a test of whether the coefficients in two linear regressions on different data sets are equal. In econometrics, it is most commonly used in time series analysis to test for the presence of a structural break at a period which can be assumed to be known a priori (for instance, a major historical event such as a war). In program evaluation, the Chow test is often used to determine whether the independent variables have different impacts on different subgroups of the population.

As shown in the figure below, regressions on the 2 sub-intervals seem to have greater explanatory power than a single regression over the data.

440px-chow_test_structural_break

For the data above, determining the sub-intervals is an easy task. However, things may not look that simple in reality. Conducting a Chow test for structural breaks leaves the data scientist at the mercy of his subjective gaze in choosing a null hypothesis for a break point in the data.

Instead of choosing the breakpoints in an exogenous manner, what if the data itself could learn where these breakpoints lie? Such an endogenous technique is what Bai and Perron came up with in a seminal paper published in 1998 that could detect multiple structural breaks in longitudinal data. A later paper in 2003 dealt with the testing for breaks empirically, using a dynamic programming algorithm based on the Bellman principle.

I will discuss a quick implementation of this technique in R.

Brief Outline:

Assuming you have a ts object (I don’t know whether this works with zoo, but it should) in R, called ts. Then implement the following:

An illustration 

I started with data on India’s rice crop productivity between 1950 (around Independence from British Colonial rule) and 2008. Here’s how it looks:

rice_productivity

You can download the excel and CSV files here and here respectively.

Here’s the way to go using R:

Voila, this is what you get:

02_rice_multiplebreaks

The dotted vertical lines indicated the break dates; the horizontal red lines indicate their confidence intervals.

This is a quick and dirty implementation. For a more detailed take, check out the documentation on the R package called strucchange.

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MITx 15.071x (Analytics Edge) – 2016

I am auditing this course currently and just completed its 2nd assignment. It’s probably one of the best courses out there to learn R in a way that you go beyond the syntax with an objective in mind – to do analytics and run machine learning algorithms to derive insight from data. This course is different from machine learning courses by say, Andrew Ng in that this course won’t focus on coding the algorithm and rather would emphasize on diving right into the implementation of those algorithms using libraries that the R programming language already equips us with.

Take a look at the course logistics. And hey, they’ve got a Kaggle competition!

AnalyticsEdgeLogistics

There’s still time to enroll and grab a certificate (or simply audit). The course is offered once a year. I met a bunch of people who did well at a data hackathon I had gone to recently, who had learned the ropes in data science thanks to Analytics Edge.

Detecting Structural Breaks in China’s FX Regime

Edit: This post is in its infancy. Work is still ongoing as far as deriving insight from the data is concerned. More content and economic insight is expected to be added to this post as and when progress is made in that direction.

This is an attempt to detect structural breaks in China’s FX regime using Frenkel Wei regression methodology (this was later improved by Perron and Bai). I came up with the motivation to check for these structural breaks while attending a guest lecture on FX regimes by Dr. Ajay Shah delivered at IGIDR. This is work that I and two other classmates are working on as a term paper project under the supervision of Dr. Rajeswari Sengupta.

The code below can be replicated and run as is, to get same results.

As can be seen in the figure below, the structural breaks correspond to the vertical bars. We are still working on understanding the motivations of China’s central bank in varying the degree of the managed float exchange rate.

strucchange_china_2006_2010

EDIT (May 16, 2016):

The code above uses data provided by the package itself. If you wished to replicate this analysis on data after 2010, you will have to use your own data. We used Quandl, which lets you get 10 premium datasets for free. An API key (for only 10 calls on premium datasets) is provided if you register there. Foreign exchange rate data (2000 onward till date) apparently, is premium data. You can find these here.

Here are the (partial) results and code to work the same methodology on the data from 2010 to 2016:

20102016

We got breaks in 2010 and in 2015 (when China’s stock markets crashed). We would have hoped for more breaks (we can still get them), but that would depend on the parameters chosen for our regression.

 

Data Manipulation in R with dplyr – Part 3

This happens to be my 50th blog post – and my blog is 8 months old.

🙂

This post is the third and last post in in a series of posts (Part 1Part 2) on data manipulation with dlpyr. Note that the objects in the code may have been defined in earlier posts and the code in this post is in continuation with code from the earlier posts.

Although datasets can be manipulated in sophisticated ways by linking the 5 verbs of dplyr in conjunction, linking verbs together can be a bit verbose.

Creating multiple objects, especially when working on a large dataset can slow you down in your analysis. Chaining functions directly together into one line of code is difficult to read. This is sometimes called the Dagwood sandwich problem: you have too much filling (too many long arguments) between your slices of bread (parentheses). Functions and arguments get further and further apart.

The %>% operator allows you to extract the first argument of a function from the arguments list and put it in front of it, thus solving the Dagwood sandwich problem.

group_by()

group_by() defines groups within a data set. Its influence becomes clear when calling summarise() on a grouped dataset. Summarizing statistics are calculated for the different groups separately.

Combine group_by with mutate

group_by() can also be combined with mutate(). When you mutate grouped data, mutate() will calculate the new variables independently for each group. This is particularly useful when mutate() uses the rank() function, that calculates within group rankings. rank() takes a group of values and calculates the rank of each value within the group, e.g.

rank(c(21, 22, 24, 23))

has output

[1] 1 2 4 3

As with arrange(), rank() ranks values from the largest to the smallest and this behaviour can be reversed with the desc() function.

 

 

My First Data Science Hackathon

So after 8 months of playing around with R and Python and blog post after blog post, I found myself finally hacking away at a problem set from the 17th storey of the Hindustan Times building at Connaught Place. I had entered my first ever data science hackathon conducted by Analytics Vidhya, a pioneer in analytics learning in India. Pizzas and Pepsi were on the house. Like any predictive analysis hackathon, this one accepted unlimited entries till submission time. It was from 2pm to 4:30pm today –  2.5 hours, of which I ended up wasting 1.5 hours trying to make my first submission which encountered submission error after submission error until the problem was fixed finally post lunch. I had 1 hour to try my best. It wasn’t the best performance, but I thought of blogging this experience anyway, as a reminder of the work that awaits me. I want to be the one winning prize money at the end of the day.

🙂

screenshot-datahack analyticsvidhya com 2015-12-20 18-41-12

 

Data Manipulation in R with dplyr – Part 2

Note that this post is in continuation with Part 1 of this series of posts on data manipulation with dplyr in R. The code in this post carries forward from the variables / objects defined in Part 1.

In the previous post, I talked about how dplyr provides a grammar of sorts to manipulate data, and consists of 5 verbs to do so:

The 5 verbs of dplyr
select – removes columns from a dataset
filter – removes rows from a dataset
arrange – reorders rows in a dataset
mutate – uses the data to build new columns and values
summarize – calculates summary statistics

I went on to discuss examples using select() and mutate(). Let’s now talk about filter(). R comes with a set of logical operators that you can use inside filter(). These operators are:
x < y, TRUE if x is less than y
x <= y, TRUE if x is less than or equal to y
x == y, TRUE if x equals y
x != y, TRUE if x does not equal y
x >= y, TRUE if x is greater than or equal to y
x > y, TRUE if x is greater than y
x %in% c(a, b, c), TRUE if x is in the vector c(a, b, c)

The following call, for example, filters df such that only the observations where the variable a is greater than the variable b:
filter(df, a > b)

Combining tests using boolean operators
R also comes with a set of boolean operators that you can use to combine multiple logical tests into a single test. These include & (and), | (or), and ! (not). Instead of using the & operator, you can also pass several logical tests to filter(), separated by commas. The following calls equivalent:

filter(df, a > b & c > d)
filter(df, a > b, c > d)

The is.na() will also come in handy very often. This expression, for example, keeps the observations in df for which the variable x is not NA:

filter(df, !is.na(x))

A recap on select(), mutate() and filter():

Arranging Data
arrange() can be used to rearrange rows according to any type of data. If you pass arrange() a character variable, R will rearrange the rows in alphabetical order according to values of the variable. If you pass a factor variable, R will rearrange the rows according to the order of the levels in your factor (running levels() on the variable reveals this order).

By default, arrange() arranges the rows from smallest to largest. Rows with the smallest value of the variable will appear at the top of the data set. You can reverse this behaviour with the desc() function. arrange() will reorder the rows from largest to smallest values of a variable if you wrap the variable name in desc() before passing it to arrange()

Summarizing Data

summarise(), the last of the 5 verbs, follows the same syntax as mutate(), but the resulting dataset consists of a single row instead of an entire new column in the case of mutate().

In contrast to the four other data manipulation functions, summarise() does not return an altered copy of the dataset it is summarizing; instead, it builds a new dataset that contains only the summarizing statistics.

Note: summarise() and summarize() both work the same!

You can use any function you like in summarise(), so long as the function can take a vector of data and return a single number. R contains many aggregating functions. Here are some of the most useful:

min(x) – minimum value of vector x.
   max(x) – maximum value of vector x.
mean(x) – mean value of vector x.
median(x) – median value of vector x.
quantile(x, p) – pth quantile of vector x.
  sd(x) – standard deviation of vector x.
var(x) – variance of vector x.
IQR(x) – Inter Quartile Range (IQR) of vector x.
diff(range(x)) – total range of vector x.

dplyr provides several helpful aggregate functions of its own, in addition to the ones that are already defined in R. These include:

first(x) – The first element of vector x.
last(x) – The last element of vector x.
nth(x, n) – The nth element of vector x.
n() – The number of rows in the data.frame or group of observations that summarise() describes.
n_distinct(x) – The number of unique values in vector x

This would be it for Part-2 of this series of posts on data manipulation with dplyr. Part 3 would focus on the pipe operator, Group_by and working with databases.

Data Manipulation in R with dplyr – Part 1

dplyr is one of the packages in R that makes R so loved by data scientists. It has three main goals:

  1. Identify the most important data manipulation tools needed for data analysis and make them easy to use in R.
  2. Provide blazing fast performance for in-memory data by writing key pieces of code in C++.
  3. Use the same code interface to work with data no matter where it’s stored, whether in a data frame, a data table or database.

Introduction to the dplyr package and the tbl class
This post is mostly about code. If you’re interested in learning dplyr I recommend you type in the commands line by line on the R console to see first hand what’s happening.

Select and mutate
dplyr provides grammar for data manipulation apart from providing data structure. The grammar is built around 5 functions (also referred to as verbs) that do the basic tasks of data manipulation.

The 5 verbs of dplyr
select – removes columns from a dataset
filter – removes rows from a dataset
arrange – reorders rows in a dataset
mutate – uses the data to build new columns and values
summarize – calculates summary statistics

dplyr functions do not change the dataset. They return a new copy of the dataset to use.

To answer the simple question whether flight delays tend to shrink or grow during a flight, we can safely discard a lot of the variables of each flight. To select only the ones that matter, we can use select()

dplyr comes with a set of helper functions that can help you select variables. These functions find groups of variables to select, based on their names. Each of these works only when used inside of select()

  • starts_with(“X”): every name that starts with “X”
  • ends_with(“X”): every name that ends with “X”
  • contains(“X”): every name that contains “X”
  • matches(“X”): every name that matches “X”, where “X” can be a regular expression
  • num_range(“x”, 1:5): the variables named x01, x02, x03, x04 and x05
  • one_of(x): every name that appears in x, which should be a character vector

In order to appreciate the usefulness of dplyr, here are some comparisons between base R and dplyr

mutate() is the second of the five data manipulation functions. mutate() creates new columns which are added to a copy of the dataset.

So far we have added variables to hflights one at a time, but we can also use mutate() to add multiple variables at once.