1. Time Series Analysis
By Tyler Moore

2. What Is Time Series Data
An ordered sequence of values of a variable at equally spaced time intervals
Used for:
Obtaining an understanding of underlying forces and structure that produced the observed data
Used primarily for forecasting and signal detection and estimation

3. Forecasting: Moving Average
Used to gain better information on trends going on in data
Moving average: break down time periods into smaller components
Using just the average can be a poor way of modeling future expectations

4. Forecasting: Smoothing
Assigns expontentially smaller weights to older observations.
Allows for better analysis of trends
Single, double(trends), and triple (trends and seasonality)
Ex: triple exponential smoothing
Use if data shows trend and seasonality
Called the Holt-Winters Method

5. Box-Jenkins Models
Combination of Moving Average, and Autoregressive Models
Autoregressive model: Linear regression of current value against one or more prior values
3 stages:
Model Identification
Model Estimation
Model Validation

6. Model Identification
Assess stationarity and seasonality

7. Model Identification
Identify order for autoregressive and moving average terms
Autocorrelation or partial autocorrelation plot

8. Example
No seasonality
Appears stationary

9. Example Continued
Values alternate in sign and drop off after lag 2 meaning we use AR(2) model
Means we use 2 predictors

10. Example Continued

11. Signal Detection and Estimation
EEG and fMRI data fall under this category

12. References
Hamilton, J. D. (1994). Time series analysis (Vol. 2). Princeton: Princeton university press.
NIST/SEMATECH e-Handbook of Statistical Methods, 25, 2016.