Time Series Pt. 1 Flashcards
What are time series models?
Sequence of data points, which are successive measurements made over a time interval. We analyze what has happened in the past and using it to predict the future. We make assumptions about the underlying generating process for our data and project this behavior forward
What is white noise?
When variables are independent and identically distributed so has no correlation with other variables. The mean is zero and has constant variance.
What happens if your time series data is white noise?
It is completely random and thus not going to be very good for predictors. On the other hand, if the series of errors from time series model are white noise, then you did a good job of fitting the model.
Three characteristics of time series models that make them predictive
- Stationarity
- Seasonality
- Target Variable Autocorrelation
Stationarity
Observations’ statistical properties stay constant over time (mean and variance stay constant)
Seasonality
Observations fluctuate periodically through time
Target Variable Autocorrelation
Observations that are close together in time tend to be correlated. Time series model tends to explain these serial correlation
Trend Component
Long term, slow evolution of the time series. Trends will either be deterministic or stochastic
Random Component
Corresponds to the short-term fluctuation, which is often difficult to predict
What is differencing?
A method in which we data transform to make stationary
Lag
Number of “time steps” between data points
Backwards Shift Operator (lag operator)
B takes a time series element and returns the element one time unit previously
Difference Operator
Used in non-stationary models – change takes a time series element and returns the difference between the element and that of one-time unit previously
