September 17, 2014

How to Compute Moving Average in R Language

A moving average is used to smooth out a time series. Computing moving average is a typical case of ordered data computing. Its basic computing method is to create a subset composed of N consecutive members of a time series, compute the average of the set and shift the subset forward one by one. The following example teaches you how to compute moving average in R language.

Case description:

Data frame sales has two fields: salesDate and Amount of this date. Requirement: compute the moving average in three days. Computing steps include seeking sales amount average of the previous day, the current day and the next day, and shift forward along the dates. A part of the source data is as follows:
Computed result:
Code interpretation:
filter function can be used in R language to compute moving average, which produces concise code. This method is quite convenient.

Despite the convenience of the filter function, it is difficult to understand for beginners. For example, sales$Amount/3means dividing the current value of field Amount by three,but when it is used in filter function, it may mean adding the three consecutive values together, then divide the sum by three. [1,1,1] is the value of expression rep(1,3), which is used here to specify the range of data fetching. In addition, because neither the name nor the parameters of filter function contain the words “average” and “moving”, even many developers of R language don’t know its use for computing moving average.

In fact, filter function is a universal linear filter. Its use is more than computing moving average. Its complete function reference is filter(x, filter, method = c("convolution", "recursive"),sides = 2, circular = FALSE, init).
Any modification of the requirement will make the code more difficult to understand. For example, the code for computing moving average of the current day and the previous two days cannot be written as filter(sales$Amount/3, rep(0,2)), it has to befilter(sales$Amount/3, rep(1,3), sides = 1).
R language can compute moving average, but its code is rather elusive.

Third-party solutions
We can also use Python, esProc and Perl to handle this case. As R language, all of these languages can perform data statistics and analysis and compute moving average. The following introduces solutions of Python and esProc briefly.

Pandas is Python's third-party library function. It is powerful in processing structured data with basic data type imitating R's data frame. At present the latest version is 0.14. Its code for handling this case is as follows:
         pandas.stats.moments.rolling_mean(sales["Amount"], 3)

The name of rolling_mean function is clear, even a developer without experience with pandas can understand it easily. The function’s usage is simple too. Its first parameter is the sequence being computed and the second parameter is N, which is the number of days in seeking moving average.

esProc is good at expressing business logic freely with agile syntax. Its expressions for relative position can solve computational problems of ordering data easily. The code is as follows:

{-1,1} in the code represents a relative interval, that is, the three days of the previous day, the current day and the next day. It can be seen that moving average can be worked out clearly and flexibly by using a relative interval. If it is required, for example, to compute the moving average of the current day and the previous two days, we just need to change the interval to {-2,0}in esProc.

A relative interval is a set. esProc can also express an element of relative position. For example, it can compute sales growth rate with (Amount -Amount[-1]) conveniently. In contrast, the code in R language and Python is difficult to understand.