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4.
TIME SERIES
4. You are given the following information about an AR(1) model with mean...
explain which time series model is more likely to describe the time series, an AR(1), AR(2),...
explain which time series model is more likely to describe the
time series, an AR(1), AR(2), MA(1) or MA(2) process? Justify your
answer
Sample: 1983 2017 Included observations: 35 Autocorrelation Partial Correlation AC PAC Q-Stat Prob 1 1 I 1 1 inta I 1 1 0.517 0.517 10.164 0.001 2 0.234 -0.044 12.318 0.002 3 0.234 0.178 14.526 0.002 4 0.158 -0.041 15.570 0.004 5 0.216 0.193 17.576 0.004 6 0.281 0.103 21.098 0.002 7 0.106 -0.144 21.619 0.003 8...
Below you are given the first four values of a time series. Time Period Time Series...
Below you are given the first four values of a time series. Time Period Time Series Value 1 18 2 20 25 17 Using a fourth-order moving average, the forecasted value for period 5 is 2.5 20 O 17 10
9. The AR(2) model is to be fit to a zero mean series, The first three sample autocovariances fro...
9. The AR(2) model is to be fit to a zero mean series, The first three sample autocovariances from N:-1000 observations are known to be 'W (0) 3.6840,า), (1) -: 2.2918, and 'W(2)-1.8491. Using Yule-Walker estimation methods, estimate all model parameters, including the IID noise variance σ
9. The AR(2) model is to be fit to a zero mean series, The first three sample autocovariances from N:-1000 observations are known to be 'W (0) 3.6840,า), (1) -: 2.2918, and 'W(2)-1.8491....
A) Discuss what the time series decomposition tells you about your data series. Include discussio...
a) Discuss what the time series decomposition tells you about
your data series. Include discussion of the seasonal, cyclical, and
trend components.
b) Compare the time series decomposition forecasts with Holt
Winters. Within the sample, is the times series decomposition or
Holt Winters more accurate? Try to explain why. (see below for
data)
Audit Trail- Statistics Accuracy Measures MAPE R-Square Value 1.65% 98.99% Forecast Statistics Mean Standard Deviation Value 5.06 1.04 Method Statistics Method Selected Basic Method Decomposition type Value...
Q3. [10 points [Serial Correlation Consider a simple linear regression model with time series dat...
Q3. [10 points [Serial Correlation Consider a simple linear regression model with time series data: Suppose the error ut is strictly exogenous. That is Moreover, the error term follows an AR(1) serial correlation model. That where et are uncorrelated, and have a zero mean and constant variance a. 2 points Will the OLS estimator of P be unbiased? Why or why not? b. [3 points Will the conventional estimator of the variance of the OLS estimator be unbiased? Why or...
3. We obtain autocorrelation function of residuals of the five autoregressive models: AR(1), AR(2), AR(3), AR(4)...
3. We obtain autocorrelation function of residuals of the five autoregressive models: AR(1), AR(2), AR(3), AR(4) and AR(5). Choose a model that performs reasonably well, according to the plots of autocorrelation function. Explain the reason (no more than 20 words.) Autocorrelation function for AR(1) model Series ar1$residuals 1.0 RO 0.6 ACF 0.4 -0.2 0.0 0.2 0 5 10 15 Lag Autocorrelation function for AR(2) model Serles ar2$residuals 1.0 RO 0.6 ACF 0.4 -0.2 0.0 0.2 0 5 10 15 Lag...
You obtain the first 5 autocorrelations and their p-values for a certain time series dataset: Order...
You obtain the first 5 autocorrelations and their p-values for a certain time series dataset: Order Autocorrelation P-value 1st 5.03 0.001 2nd 4.89 0.005 3rd 4.77 0.007 4th 0.31 0.787 5th 0.27 0.803 What would be your best guess for the model that fits this data? An MA(3) model An MA(2) model An MA(1) model An AR(1) model An ARMA(1,2) model
5) The following MINITAB output is for ARIMA model of certain time series of size 132....
5) The following MINITAB output is for ARIMA model of certain time series of size 132. Type AR 1 AR 2 SAR 12 -0.27124 0.0662 1.590.113 Constant 0.074870.08826 -3.07 0.0026 Coef 0.62993 0.07249 8.69 0.001 0.20816 0.07344 2.83 0.0053 SE Residuals: SS-0.0002323 MS- 0.001409, DE=117 Modified Box-Pierce (Ljung-Box) Chi-square statistio Lag Chi-Square 8.6 15.4 28.038.7 DE P-Value 0.3859 0.7635 0.7029 0.6014 12 24 36 8 7 31 43 Which parameters should be included in the model and why? Based on...
Using the following completed regression model AR(1) with correlated residuals: Y. =-10+25x, in which p=.5 is...
Using the following completed regression model AR(1) with correlated residuals: Y. =-10+25x, in which p=.5 is the correlation coefficient between time ordered residuals. Given the following data: St 1 X 10 30 60 unknown 3 . Using the Hildreth Lu method , forecast the value of Yt for X=4.
time series 3. Specify and interpret the model in terms of a time- series data Xt...
time series
3. Specify and interpret the model in terms of a time- series data Xt for the following multiplicative models ARIMA: (1, 0, 0)(1, 0, 0)4 ARIMA (0, 1, 0)(1, 1, 0)6 ARIMA (0, 1, 1)(0, 0, 1)12
explain which time series model is more likely to describe the
time series, an AR(1), AR(2), MA(1) or MA(2) process? Justify your
answer
Sample: 1983 2017 Included observations: 35 Autocorrelation Partial Correlation AC PAC Q-Stat Prob 1 1 I 1 1 inta I 1 1 0.517 0.517 10.164 0.001 2 0.234 -0.044 12.318 0.002 3 0.234 0.178 14.526 0.002 4 0.158 -0.041 15.570 0.004 5 0.216 0.193 17.576 0.004 6 0.281 0.103 21.098 0.002 7 0.106 -0.144 21.619 0.003 8...
Below you are given the first four values of a time series. Time Period Time Series Value 1 18 2 20 25 17 Using a fourth-order moving average, the forecasted value for period 5 is 2.5 20 O 17 10
9. The AR(2) model is to be fit to a zero mean series, The first three sample autocovariances from N:-1000 observations are known to be 'W (0) 3.6840,า), (1) -: 2.2918, and 'W(2)-1.8491. Using Yule-Walker estimation methods, estimate all model parameters, including the IID noise variance σ
9. The AR(2) model is to be fit to a zero mean series, The first three sample autocovariances from N:-1000 observations are known to be 'W (0) 3.6840,า), (1) -: 2.2918, and 'W(2)-1.8491....
a) Discuss what the time series decomposition tells you about
your data series. Include discussion of the seasonal, cyclical, and
trend components.
b) Compare the time series decomposition forecasts with Holt
Winters. Within the sample, is the times series decomposition or
Holt Winters more accurate? Try to explain why. (see below for
data)
Audit Trail- Statistics Accuracy Measures MAPE R-Square Value 1.65% 98.99% Forecast Statistics Mean Standard Deviation Value 5.06 1.04 Method Statistics Method Selected Basic Method Decomposition type Value...
Q3. [10 points [Serial Correlation Consider a simple linear regression model with time series data: Suppose the error ut is strictly exogenous. That is Moreover, the error term follows an AR(1) serial correlation model. That where et are uncorrelated, and have a zero mean and constant variance a. 2 points Will the OLS estimator of P be unbiased? Why or why not? b. [3 points Will the conventional estimator of the variance of the OLS estimator be unbiased? Why or...
3. We obtain autocorrelation function of residuals of the five autoregressive models: AR(1), AR(2), AR(3), AR(4) and AR(5). Choose a model that performs reasonably well, according to the plots of autocorrelation function. Explain the reason (no more than 20 words.) Autocorrelation function for AR(1) model Series ar1$residuals 1.0 RO 0.6 ACF 0.4 -0.2 0.0 0.2 0 5 10 15 Lag Autocorrelation function for AR(2) model Serles ar2$residuals 1.0 RO 0.6 ACF 0.4 -0.2 0.0 0.2 0 5 10 15 Lag...
5) The following MINITAB output is for ARIMA model of certain time series of size 132. Type AR 1 AR 2 SAR 12 -0.27124 0.0662 1.590.113 Constant 0.074870.08826 -3.07 0.0026 Coef 0.62993 0.07249 8.69 0.001 0.20816 0.07344 2.83 0.0053 SE Residuals: SS-0.0002323 MS- 0.001409, DE=117 Modified Box-Pierce (Ljung-Box) Chi-square statistio Lag Chi-Square 8.6 15.4 28.038.7 DE P-Value 0.3859 0.7635 0.7029 0.6014 12 24 36 8 7 31 43 Which parameters should be included in the model and why? Based on...
Using the following completed regression model AR(1) with correlated residuals: Y. =-10+25x, in which p=.5 is the correlation coefficient between time ordered residuals. Given the following data: St 1 X 10 30 60 unknown 3 . Using the Hildreth Lu method , forecast the value of Yt for X=4.
time series
3. Specify and interpret the model in terms of a time- series data Xt for the following multiplicative models ARIMA: (1, 0, 0)(1, 0, 0)4 ARIMA (0, 1, 0)(1, 1, 0)6 ARIMA (0, 1, 1)(0, 0, 1)12
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