# Essay on Time Series Arima Project

2779 Words Nov 10th, 2014 12 Pages
Predicting Initial Claims Using ARIMA models

I. Introduction

Initial claims is a measure of the number of jobless claims filed by individuals seeking to receive state jobless benefits. This number is watched closely by financial analysts because it provides insight into the direction of the economy. Higher initial claims correlate with a weakening economy.

According to Investopedia.com, the strength of a nation's economy will have an impact on the appreciation or depreciation of its currency against other major currencies. Therefore, forex traders typically look at the initial claims figure as part of their analyses when assessing a currency's prospects for the immediate future. Generally speaking, week-by-week numbers are too
Because no clear order can be seen from these plots, I decided to take the first difference of the data.

Now, looking at the first difference of the weekly initial unemployment claims, the data seems to be a little smoother but still contains some outliers. Now, there seems to be a more discernible order in the data, and once again, it does not follow a white noise process as seen by the ACF and PACF plots.

I put these plots again just so that the plots can be a little bit more visible to see the reason behind why I chose the models below. III. Model Estimation

From the ACF and PACF plots, I surmise that the data can fit a number of ARMA models: * ARMA(0,1) MA(1) * ARMA(0,3) MA(3) * ARMA(10,0) AR(10) * ARMA(12,0) AR(12) * ARMA(14,0) AR(14) * ARMA(19,0) AR(19) * ARMA(10,1) * ARMA(10,3) * ARMA(12,1) * ARMA(12,3) * ARMA(14,1) * ARMA(14,3) * ARMA(19,1) * ARMA(19,3)

Now, I used R to perform some preliminary estimation of the parameters of the above models to the differenced data. After doing this estimation, some of the models I retained and some I rejected based on the ratio test of significance of the coefficients. The reasons are: * ARMA(0,1) MA(1) – retained * ARMA(0,3) MA(3) – retained * ARMA(10,0) AR(10) – retained * ARMA(12,0) AR(12) – retained * ARMA(14,0)

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