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Exponential Smoothing

Presentation transcript:

Exponential Smoothing

Forecasting - Qualitative vs. quantitative methods 1 These methods are usually applied to short- or intermediate-range decisions. Examples of quantitative forecasting methods are last period demand, simple and weighted N-Period moving averages, simple exponential smoothing, and multiplicative seasonal indexes.

Low-pass filter - Laplace notation 1 This exponential smoothing property matches the exponential function|exponential decay seen in the continuous-time system

Exponential smoothing 1 Whereas in the simple moving average the past observations are weighted equally, exponential smoothing assigns exponentially decreasing weights over time.

Exponential smoothing 1 Exponential smoothing is commonly applied to financial market and economic data, but it can be used with any discrete set of repeated measurements. The raw data sequence is often represented by, and the output of the exponential smoothing algorithm is commonly written as, which may be regarded as a best estimate of what the next value of x will be. When the sequence of observations begins at time t=0, the simplest form of exponential smoothing is given by the formulae:

Exponential smoothing - The exponential moving average 1 Exponential smoothing was first suggested by Robert Goodell Brown in 1956, and then expanded by Charles C. Holt in reprinted in The formulation below, which is the one commonly used, is attributed to Brown and is known as Brown's simple exponential smoothing.

Exponential smoothing - The exponential moving average 1 where α is the smoothing factor, and 00 based on the raw data up to time t. Double exponential smoothing is given by the formulas

Exponential smoothing - The exponential moving average 1 And for t α0 based on the raw data up to time t. Triple exponential smoothing is given by the formulas

Pricing science - Forecasting time-phased demand 1 Forecasting methods generally fall into the class of methods known as time series methods, primarily exponential smoothing, or causal methods, where price is taken to be (one of) the causal factors

Pricing science - Forecasting granular demand 1 'Kalman Filtering and Exponential Smoothing'

Pricing science - Accounting for censoring 1 Conventionally, these methods are referred to as unconstraining methods, include manual adjustment, averaging methods, Expectation maximization|Expectation Maximization (EM) methods, exponential smoothing methods.Crystal, C., Ferguson, M., Higbie, J., Kapoor, R

Predictive Model Markup Language - PMML 4.0, 4.1 and * Time Series Models: New exponential Smoothing models; also place holders for ARIMA, Seasonal adjustment|Seasonal Trend Decomposition, and Spectral density estimation, which are to be supported in the near future.

Autoregressive integrated moving average - Implementations in statistics packages 1 The default Expert Modeler feature evaluates a range of seasonal and non- seasonal autoregressive (p), integrated (d), and moving average (q) settings and seven exponential smoothing models

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