6. Given the following sample autocorrelations and partial autocorrelations for
ID: 3340607 • Letter: 6
Question
6. Given the following sample autocorrelations and partial autocorrelations for a sample of 100 observations from actual data 4 7 Lag acf 0.420-0.104 0.032 0.206 0.138 0.042 0.074 -0.018 pcf 0.632 0.381 0.268 0.199 0.205 0.101 0.096 0.082 a. Identify the most appropriate time series process for this data. b. Use the Ljung-Box Q* test to determine whether the first three autocorrelation coefficients taken together are jointly significantly different from zero. State the null hypothesis. [10 marks]Explanation / Answer
a) ACF(auto corelation) is basically a linear dependance of a variable with itself at 2 different time intervals. Whereas PACF(partial auto correlation) is as the name suggest is partial and not full. The most appropriate time series would be when the p value is greater thatn 0.05, hence it will be when the lag is 1.
b)In Ljung Box test the null hypothesisi is that the first n ACF should be jointly zero. If we summ up the first 3 ACF coffecient jointly is different from zero which proves our Null hyposthesis.
The sample autocorrelation function (ACF) and partial autocorrelation function (PACF) are useful qualitative tools to assess the presence of autocorrelation at individual lags. The Ljung-Box Q-test is a more quantitative way to test for autocorrelation at multiple lags jointly
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.