Question

1.
General features of economic time series: trends, cycles, seasonality.
2.
Simple linear regression model and multiple regression model: dependent variable, regressor, error term; fitted value, residuals; interpretation.
3.
Population VS sample: a sample is a subset of a population.
4.
Estimator VS estimate.
5.
For what kind of models can we use OLS?
6.
R-squared VS Adjusted R-squared.
7.
Model selection criteria: R-squared/Adjusted R-squared; residual variance; AIC, BIC.
8.
Hypothesis testing: p-value, confidence interval (CI), (null hypothesis , significance level, test statistic).
9.
Stochastic process VS time series.
10.
Basic notations.
11.
For a time series, can we compute a time mean and a time variance?
12.
Stationarity of a stochastic process: strongly stationary, 1st order weakly stationary, 2nd order weakly stationary/covariance-stationary.
13.
Can we transform a non-stationary process into a 1st order weakly stationary or 2nd order weakly stationary/covariance-stationary process?
14.
How to derive a return from a time series?
15.
Auto-correlation function (ACF, ) VS partial auto-correlation function (PACF, ).
16.
Hypothesis testing for ACF: individually VS jointly, (null hypothesis, significance level, test statistic).
17.
Information set, forecast horizon, loss function; examples of 1-step-ahead forecast of a stochastic process.
18.
Short-term VS long-term forecasts, low-frequency VS high-frequency time series data, short memory VS long memory process.
19.
In-sample assessment of the goodness of the model, out-of-sample assessment of the forecasting ability of the model.
20.
Three ways to divide the sample into estimation sub-sample and prediction sub-sample. Ch5, Ch6
21.
Basic models: MA(q), AR(p), ARMA(p, q). a. Definition of each model; b. Definition of a white noise process.
22.
Wold Decomposition Theorem. a. We can always find a unique linear model to represent a covariance stationary process.
23.
Lag operators.
24.
Invertibility of an MA process. a. Why we need to check the invertibility property of an MA process? b. How to check the invertibility property of an MA(1) process?
25.
Covariance stationality of MA process. a. Finite MA processes are always stationary. b. Condition for the invertibility of an MA(1) process.
c.
Condition for the invertibility of an MA process of high order.
26.
Derive 1-step-ahead optimal forecast and forecast error of an MA(1) process.
27.
Based on correlogram, write down MA(q) model.  

Answer 1

1.

Time series is the method of analyzing data for future prediction, estimation, and forecasting. The types of such analyzing are trend, cycle, and seasonal.

Features are as below:

Trend: This is the long-term analyzing of data, which gives estimation for future. If the trend is increasing, such estimation should also be increased; or vice versa.

Cycle: This is the short-period rotation of ups and downs of data analyzing. It gives idea when will be the cycle starts and ends in future. Usually it takes to complete a rotation around 2.5 year time.

Seasonal: This is all those fixed periods when data used to increase. Example is increasing revenue on Christmas time. Such data are highly predictable in future year too. Seasonal factors are festive season, winter season, year-end season, etc.