Suppose we have a stationary process: yt=
Suppose we have a stationary process: yt=β₀+β₁yt-1+ut and ut follows the standard normal distribution.
Explain what is the meaning of stationarity.
Show the expected value and variance of yt.
R² is always increased whenever we include the lags and can we include the lags as much as possible?
How to choose the number of lags p in an A R(p) ?
Are the forecasts from the time series model the OLS predicted values? Why?
Compute the 1st and 2nd autocovariance of yt.
Compute the 1st and 2nd autocorrelation of yt.
What is the difference between BIC and AIC?
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2. Suppose that Ya ut where the ut are iid Normal with mean zero and variance σ2, but that you mistakenly think Yt is difference stationary. You therefore construct a new series a) Are the Xt i.i.d.?...
2. Suppose that Ya ut where the ut are iid Normal with mean zero and variance σ2, but that you mistakenly think Yt is difference stationary. You therefore construct a new series a) Are the Xt i.i.d.? Explain b) Is X stationary? Explain c) Calculate the mean, variance, and autocorrelation function of X d) How does the answer you obtained in (c) compare with the mean, variance and autocor- relation function of Y?
2. Suppose that Ya ut where the...
Suppose that we believe a weakly stationary return sequence r following the model, where at ls...
Suppose that we believe a weakly stationary return sequence r following the model, where at ls the 1.1.d. noise sequence with mean 0 and variance σ. and at s independent of rt-1,Tt-2. (a) Express the mean μ of the return sequence rt using φο, φι, φ2 and σ (lag-0 autocovariance) of r) (d) Express the lag-1 autocorrelation ρι using φο, φι, φ2 and σ
Exercise 6,7,8, and 9 use data from exercise 5 for exercise 6. use data from the...
Exercise 6,7,8, and 9
use data from exercise 5 for exercise 6.
use data from the graph for 7,8,9
d. LY, for some integer k> 0 5. The following table contains quarterly nominal GDP in U.S. (billions of dol- lars). Let Y, denote the GDP at time t and let y, = ln (Y). (Show your calculations in a spreadsheet, e.g., in Microsoft Excel.) a. Plot the time series (Y). Can the underlying stochastic process be weakly b. Calculate the...
Which one of the following is a good candidate to forecast the cyclical component for the future?...
Which one of the following is a good candidate to forecast the cyclical component for the future? HES SES WES All of the above In OLS, deviations of predicted values from actual values are called Residuals Population errors Random deviations All of the above When computing the MAt, _________ is(are) removed Seasonality and irregular fluctuations Seasonality, irregular fluctuations, and cyclical movements Seasonality and cyclical movements Irregular fluctuations and cyclical movements A common source of unusual coefficient estimate signs and statistical...
Need help with stats true or false questions Decide (with short explanations) whether the following statements are true or false a) We consider the model y-Ao +A(z) +E. Let (-0.01, 1.5) be a 95% con...
Need help with stats true or false questions
Decide (with short explanations) whether the following statements are true or false a) We consider the model y-Ao +A(z) +E. Let (-0.01, 1.5) be a 95% confidence interval for A In this case, a t-test with significance level 1% rejects the null hypothesis Ho : A-0 against a two sided alternative. b) Complicated models with a lot of parameters are better for prediction then simple models with just a few parameters c)...
2. Suppose that Ya ut where the ut are iid Normal with mean zero and variance σ2, but that you mistakenly think Yt is difference stationary. You therefore construct a new series a) Are the Xt i.i.d.? Explain b) Is X stationary? Explain c) Calculate the mean, variance, and autocorrelation function of X d) How does the answer you obtained in (c) compare with the mean, variance and autocor- relation function of Y?
2. Suppose that Ya ut where the...
Suppose that we believe a weakly stationary return sequence r following the model, where at ls the 1.1.d. noise sequence with mean 0 and variance σ. and at s independent of rt-1,Tt-2. (a) Express the mean μ of the return sequence rt using φο, φι, φ2 and σ (lag-0 autocovariance) of r) (d) Express the lag-1 autocorrelation ρι using φο, φι, φ2 and σ
Exercise 6,7,8, and 9
use data from exercise 5 for exercise 6.
use data from the graph for 7,8,9
d. LY, for some integer k> 0 5. The following table contains quarterly nominal GDP in U.S. (billions of dol- lars). Let Y, denote the GDP at time t and let y, = ln (Y). (Show your calculations in a spreadsheet, e.g., in Microsoft Excel.) a. Plot the time series (Y). Can the underlying stochastic process be weakly b. Calculate the...
Need help with stats true or false questions
Decide (with short explanations) whether the following statements are true or false a) We consider the model y-Ao +A(z) +E. Let (-0.01, 1.5) be a 95% confidence interval for A In this case, a t-test with significance level 1% rejects the null hypothesis Ho : A-0 against a two sided alternative. b) Complicated models with a lot of parameters are better for prediction then simple models with just a few parameters c)...
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