ANLY482 AY2017-18T2 Group10 Analysis & Findings: Analysis
Box-Jenkins Autoregressive Integrated Moving Average (ARIMA)
In Progress
Exponential Smoothing
Exponential smoothing aims to isolate trends or seasonality from irregular variation and has been found to be most effective when the components describing the time series vary slowly as time passes [3]. In calculating the new estimate, the estimate for the current period and a portion of the current period’s generated random error are combined. Past data is weighted unequally with the effect of recent observations expected to decline exponentially as time passes
In the paper “A state space framework for automatic forecasting using exponential smoothing methods”, the authors adopt a well-established taxonomy as a framework to choose between various exponential smoothing methods [4]. This framework identifies the presence or absence of a trend component and seasonality component within the data being analysed.
To decide on the best model, we are implementing Rob J. Hyndman’s state space framework, [4] which was also covered in the literature review, that has the general notation of ETS (Error, Trend, Seasonal) Where:
- Error: The type of error function
- Trend: Function of trend
- Seasonal: Function of seasonality
Each component in the framework can either be Not present, Additive, Additive Damped, Multiplicative or Multiplicative Damped. For example the notation of ETS(A,N,N) represents Simple Exponential Smoothing - additive errors, no trend, no seasonality.
Hyndman’s framework applies each of the 24 possible exponential smoothing methods in the state space framework to our data set and decides on the best model using the AIC, BIC and AICc. In our dataset, the optimal method was ETS(M,N,N) which represents multiplicative errors with no trend and no seasonality.
