Analytical Methods

First, we check the graphical plot of the data

[pic 1]

On checking correlogram at level we find distinct AR(1) signature

[pic 2]

We conduct Unit root test and find that we cannot reject null hypothesis that there is unit root. Thus the series is non stationary.

[pic 3]

We check the correlogram at first difference and find that the series becomes white noise process. Hence we cannot de trend and proceed in this way.

[pic 4]

1st method we proceed with AR(1) process. We find that coefficient of AR(1) is below 1 and significant with p-value of t-statistics (0.000) . We also find the p-value of f-statistics is 0.000, hence the model as a whole is significant and R^2 is a respectable 0.78

[pic 5]

We check the residual diagnostic -> correlogram Q-statistics and find that the process has been converted to a white noise process. We also note that the Prob values are > 0.05

[pic 6]

We run static forecast to forecast for last 5 days. 8/9/2008 – 8/14/2008. The MAPE comes out to be 1.54%.

[pic 7]

We run dynamic forecast and get Mean Absolutute Percentage Error at 1.48%.

[pic 8]

The residual graph comes out to be

[pic 9]

Method 2

Deseasonalize the data.

Series ds=d(sen,0,5)

Check correlogram, here we see AR(1) signature and possible MA(1) signature

[pic 10]

On conducting unit root test we find that the series has turned into non stationary series, p-value of t-statistics is 0.0005

[pic 11]

We run the command

ls d(sen,0,5) AR(1) MA(1)

We find that AR(1) is significant with probability of t-statistics at 0.003, while MA(1) is insignificant.

[pic 12]

We check the correlogram for residual diagnostics and find that we are getting SMA(5) signature.

[pic 13]

We run the equation including SMA(5) and find both AR(1) and SMA(5) are significant. Coefficient of AR(1) and SMA(5) are < 1.

ls d(sen,0,5) AR(1) SMA(5)

[pic 14]

We check the residual correlogram and find that the process has been converted to white noise process, all probability values are > 0.05

[pic 15]

Next we run static forecast and find that MAPE is 0.83%

[pic 16]

We run dynamic forecast and find that MAPE is 0.91%

[pic 17]

We further check RSIDs and note the following plot

[pic 18]

Method 3

Both deseasonalize and detrend the data.

series dst=d(sen,1,5)

[pic 19]

We find distinct SMA(5) signature. We run unit root test and find that the p-value is < 0.05, thus we can reject the null hypothesis that there is a unit root. Hence the data has now become stationary.