# R Programming/Time Series

## Introduction

In the following examples we will use the data set Mpyr which is included in the R-package Ecdat, which can be loaded into R and viewed in R by the following code.

```#Installs the package Ecdat.
install.packages("Ecdat")
library(Ecdat)
#Attached the dataset Mpyr.
data(Mpyr)
#Shows the dataset Mpyr.
Mpyr
Time Series:
Start = 1900
End = 1989
Frequency = 1
m        p         y         r
1900 1.718774 2.092641 0.9030195  4.380000
1901 1.856318 2.086574 1.0131038  4.280000
1902 1.936512 2.120476 1.0114817  4.920000
```

## Creating time-series objects

• The function ts() is used to create time-series objects.
• The function as.ts() coerces an object to a time-series.
• The function is.ts() tests whether an object is a time-series.

Example:

```> data.a<-seq(1,24,by=1)
> is.ts(data.a)
[1] FALSE
> ts(data.a, start=c(2005,1), frequency=12)
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
2005   1   2   3   4   5   6   7   8   9  10  11  12
2006  13  14  15  16  17  18  19  20  21  22  23  24
> data.b<-seq(1,24,by=1)
> is.ts(data.b)
[1] FALSE
> is.ts(as.ts(data.b))
[1] TRUE
```

## Creating lagged and differenced variables

• The function lag() creates a lagged variable.
• The function diff() creates a differenced variable.

Example:

```> data.a<-seq(1,12,by=1)
> ts.a<-ts(data.a, start=c(2005,1), frequency=4)
> lag.a<-lag(ts.a,k=1)
> diff.a<-diff(ts.a,lag=1,difference=1)
> ts.a
Qtr1 Qtr2 Qtr3 Qtr4
2005    1    2    3    4
2006    5    6    7    8
2007    9   10   11   12
> lag.a
Qtr1 Qtr2 Qtr3 Qtr4
2004                   1
2005    2    3    4    5
2006    6    7    8    9
2007   10   11   12
> diff.a
Qtr1 Qtr2 Qtr3 Qtr4
2005         1    1    1
2006    1    1    1    1
2007    1    1    1    1
```

## Plotting time-series objects

• The function plot.ts() is used for plotting time-series objects.

## Fit Autoregressive Models to Time-series by OLS

In order to fit an autoregressive time series model to the data by ordinary least squares it is possible to use the function ar.ols() which is part of the "stats" package.

## Autocorrelation function

The function acf() computes (and by default plots) estimates of the autocovariance or autocorrelation function. Function pacf() is the function used for the partial autocorrelations. Function ccf() computes the cross-correlation or cross-covariance of two univariate series.[1]

## Useful R-packages

• fBasics, tis, zoo, tseries, xts, urca

## References

http://cran.r-project.org/web/views/TimeSeries.html

http://cran.r-project.org/doc/contrib/Ricci-refcard-ts.pdf