Time Series Analysis By Tyler Moore.

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Presentation transcript:

Time Series Analysis By Tyler Moore

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

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

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

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

Model Identification Assess stationarity and seasonality

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

Example No seasonality Appears stationary

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

Example Continued

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

References Hamilton, J. D. (1994). Time series analysis (Vol. 2). Princeton: Princeton university press. NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/,April 25, 2016.