STAT 520 Test 1 Review Sheet

I.  What Are Time Series Data?
  A. Key difference between time series data and cross-sectional data
  B. Scatterplots of time series values vs. lagged values to see (lag-1) autocorrelation
  C. Concept of Seasonality
  D. Displaying Multiple Time Series
II. Fundamental Mathematical Concepts
  A. Moments of a Stochastic Process
    1. Mean function E(Y_t)
    2. Variance function var(Y_t)
    3. Autocovariance function cov(Y_t, Y_s), also can be written cov(Y_t, Y_{t-k}) where k is the lag
    4. Autocorrelation function and formula relating autocorrelation to autocovariance and variance
    5. Interpretations of Autocovariance and Autocorrelation and advantages of interpreting Autocorrelation
  B. Calculating Variances, Covariance, Correlations of Linear Combinations of Random Variables
    1. "FOIL" approach
    2. How to deal with constants
  C. Simple examples of time series
    1. Random walk (definition and properties)
    2. Simple moving average (definition and properties)
  D. Writing autocovariance and autocorrelation functions as piecewise functions of the lag
  E. Concept of Stationarity
    1. Implications of being stationary of the mean function, variance function, autocovariance function
    2. Showing a process is (or is not) weakly stationary
    3. White noise process
III. Regression Trend Models for Time Series
  A. Decomposing a time series into a deterministic trend and a random noise process
  B.  Simplest Trend Model:  A constant mean
  C. Other trend models
    1. Linear time trend
    2. Estimating coefficient parameters with least squares
    3. Quadratic time trend
    4. Seasonal means model
    5. Harmonic regression model
  D. Regression Output from Software
    1. Finding estimated coefficients from software output
    2. Writing estimated trend model equation
    3. Residual standard deviation s
    4. Adjusted R^2
    5. AIC and BIC
    6. Using these criteria to selection the best trend model
  E. Residual Analyses and How to Interpret them
    1. Plots of (Standardized) Residuals against Time
    2. Plots of Residuals against Fitted Values
    3. Normal Q-Q plot of residuals
    4. Shapiro-Wilk test on residuals
    5. Runs Test on residuals
       a. What is its purpose?
       b. What is the null hypothesis?
       c. What does an excessively large number of runs indicate?  An excessively small number of runs?
    6. Sample ACF of residuals
  F. Investigating Relationships with Lagged Values of Time Series
  G. Dealing with Nonstationary Time Series
    1. Detrending
    2. Differencing
    3. Backshift Operator and how differencing tends to affect the behavior of time series
  H. Methods of Smoothing Time Series and Revealing Trends
    1. Moving Average Smoother
    2. Kernel Smoother
    3. Lowess Smoother
    4. Classical Structural Modeling breakdown of time series