CODEWITHSUNDEEP
r
http8086
http8086

Reputation: 1686

how to identify time series is stationarity or not by package fUnitRoots in R language

I have one time series, let's say

694 281 479 646 282 317 790 591 573 605 423 639 873 420 626 849 596 486 578 457 465 518 272 549 437 445 596 396 259 390

Now, I want to forecast the following values by ARIMA Model, but ARIMA requires the time series to be stationarity, so before this, I have to identify the time series above matches the requirement or not, then fUnitRoots comes up.

I think http://cran.r-project.org/web/packages/fUnitRoots/fUnitRoots.pdf can offer some help, but there is no simple tutorial

I just want one small demo to show how to identify one time series, is there any one?

thanks in advance.

Upvotes: 4

Views: 6484

Answers (2)

Metrics
Metrics

Reputation: 15458

I will give example using urca package in R. 

library(urca)
data(npext) # This is the data used by Nelson and Plosser (1982)
sample.data<-npext
head(sample.data)
 year      cpi employmt gnpdefl nomgnp interest    indprod gnpperca realgnp wages realwag sp500 unemploy velocity  M
1 1860 3.295837       NA      NA     NA       NA -0.1053605       NA      NA    NA      NA    NA       NA       NA NA
2 1861 3.295837       NA      NA     NA       NA -0.1053605       NA      NA    NA      NA    NA       NA       NA NA
3 1862 3.401197       NA      NA     NA       NA -0.1053605       NA      NA    NA      NA    NA       NA       NA NA
4 1863 3.610918       NA      NA     NA       NA  0.0000000       NA      NA    NA      NA    NA       NA       NA NA
5 1864 3.871201       NA      NA     NA       NA  0.0000000       NA      NA    NA      NA    NA       NA       NA NA
6 1865 3.850148       NA      NA     NA       NA  0.0000000       NA      NA    NA      NA    NA       NA       NA NA

I will use ADF to perform the unit root test on industrial production index as an illustration. The lag is selected based on the SIC. I use trend as there is trend in the date . 

 ############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression trend 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.31644 -0.04813  0.00965  0.05252  0.20504 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.052208   0.017273   3.022 0.003051 ** 
z.lag.1     -0.176575   0.049406  -3.574 0.000503 ***
tt           0.007185   0.002061   3.486 0.000680 ***
z.diff.lag   0.124320   0.089153   1.394 0.165695    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.09252 on 123 degrees of freedom
Multiple R-squared: 0.09796,    Adjusted R-squared: 0.07596 
F-statistic: 4.452 on 3 and 123 DF,  p-value: 0.005255 


Value of test-statistic is: -3.574 11.1715 6.5748 

Critical values for test statistics: 
      1pct  5pct 10pct
tau3 -3.99 -3.43 -3.13
phi2  6.22  4.75  4.07
phi3  8.43  6.49  5.47

#Interpretation: BIC selects the lag 1 as optimal lag. The test statistics -3.574 is less than the critical value tau3 at 5 percent (-3.430). So, the null that there is an unit root is is rejected only at 5 percent.

Also, check the free forecasting book available here

Upvotes: 4

Graeme Walsh
Graeme Walsh

Reputation: 678

You can, of course, carry out formal tests such as the ADF test, but I would suggest carrying out "informal tests" of stationarity as a first step.

Inspecting the data visually using plot() will help you identify whether or not the data is stationary.

The next step would be to investigate the autocorrelation function and partial autocorrelation function of the data. You can do this by calling both the acf() and pacf() functions. This will not only help you decide whether or not the data is stationary, but it will also help you identify tentative ARIMA models that can later be estimated and used for forecasting if they get the all clear after carrying out the necessary diagnostic checks.

You should, indeed, pay caution to the fact that there are only 30 observations in the data that you provided. This falls below the practical minimum level of about 50 observations necessary for forecasting using ARIMA models.

If it helps, a moment after I plotted the data, I was almost certain the data was probably stationary. The estimated acf and pacf seem to confirm this view. Sometimes informal tests like that suffice.

This little-book-of-r-for-time-series may help you further.

Upvotes: 1

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