Model Pre-Tests and Post-Tests

Here is a nice table detailing how to choose a model, extracted from the book: Principles of Business Forecasting Observations Residual Issue: What Visual Detection Statistical Detection Solution: How to fix Normality:ARIMA, Reg). NPP non straight diagonal Histogram non bell-shaped.  – Transformation against points Outlier Point far from: Histogram average or from NPP diagonal or from other points[…]

Causal Time Series relations

Objectives of time series analysis: – Auto-correlation: predict based on t. – Causal 1: Analyze impact of an event on a ts variable. – Causal 2:Analyze impact of a ts variable on another ts variable. Causal Time Series patterns: Challenges: 1. Explanatory and response variables may have autocorrelation within them (y & y-1, x & x-1).[…]

SAS: Using Differencing for ARIMA

Data Differencing is achieved by creating a new series which is D = Yt – Y[t-1]. Differencing aims at removing the non-stationarity in the time series, a pre-requisite for using ARIMA models against a time series. Here we explore the configuration of differencing and its impact on ACF and PACF: ARIMA configuration with D=0 Configuration[…]

SAS Time Series Exploration

SAS Time Series Exploration: We use Time series exploration to get a statistical insight about the data which helps estimating the best time series model to fit and forecast. The exploration task helps detecting stationarity through plotting, ACF, PACF and Unit Root Test results. Data setting: Data – The data set to analyze. Roles –[…]


ARIMA: Autoregression integrated Moving average. A technique used in forecasting time series. ARIMA can only work with stationary time series. Stationarity: time series has constant mean & variance & coverariance structure. Using non-stationary time series data produces unreliable and spurious results. Autocorrelation: regression of Y with Yt-p. To Test Stationarity: a. check ACF – it should drop quickly[…]

Forecasting Accuracy

Forecasting Accuracy allows evaluating the goodness of the forecast and comparing different forecasting methods. Measures for Accuracy: Mean Error Mean Percentage Error Mean Absolute Error Mean Absolute Percentage Error Root Mean Square Error Root Mean Scaled Error Theil’s U:

Exponential smoothing: SES – DES – Holt-Winter

SES: x StepAhead. a:minimize Rmse. F0:mean. OutSample. Slacked. DES: a&B. holt Linear: small period ahead. Damped T. TES: Winters: Seasonality: SI visually or by Acf. Additive/multiplicative. Deseason. MultiSeasonality. a B ¥. Outliers! We normally use Multiplicative. We only use additive qhen the data set has unstable variability, e.g. Hetero. Single Exponential Smoothing One-step ahead forecast[…]

Stationary and Auto-correlation: ARMA and ARIMA

Before conducting a regression, the “stationarity” must be checked. Correlation: consistent trend relationship between two variables. Auto-correlation: correlation between a variable Yt and Y(t-k), k being a gap in time. Auto-correlation Function ACF – ρk: Measures the auto-correlation. Partial Auto-correlation Function ACF – ρk: Measures the auto-correlation after controlling the correlations at the intermediate lags. Stationarity: time series has[…]