- "Exponential smoothing is a rule of thumb technique for smoothing time series data using the exponential window function."
A family of models that uses weighted averages of past observations to forecast the next observation.
Time series data: Time series data refers to data collected over time, which is usually represented as a sequence of consecutive observations or measurements.
Forecasting: Forecasting involves the prediction of future values of a time series based on past data, using mathematical techniques such as exponential smoothing.
Exponential smoothing: Exponential smoothing is a statistical method used for forecasting time series data, which involves smoothing the data by assigning exponentially decreasing weights to past observations.
Smoothing constants: Smoothing constants are parameters used in exponential smoothing models to determine the weight assigned to each observation in the historical data.
Simple exponential smoothing: Simple exponential smoothing is a basic form of exponential smoothing, which assigns equal weights to all past observations.
Double exponential smoothing: Double exponential smoothing, also known as Holt’s method, is an extension of simple exponential smoothing that incorporates a trend component in the forecast.
Triple exponential smoothing: Triple exponential smoothing, also known as Holt-Winters’ method, is an extension of double exponential smoothing that includes a seasonal component in the forecast.
Seasonality: Seasonality refers to cyclical patterns in time series data, which repeat themselves over a regular time interval.
Trend: Trend refers to a long-term pattern in time series data, which shows a general direction that the data is moving in over time.
Forecast error: Forecast error is the difference between the predicted value of a time series and the actual value of that series.
Mean absolute error: Mean absolute error is a measure of forecast accuracy that calculates the average absolute difference between predicted and actual values.
Mean squared error: Mean squared error is a measure of forecast accuracy that calculates the average squared difference between predicted and actual values.
Root mean squared error: Root mean squared error is a measure of forecast accuracy that calculates the square root of the mean squared error.
Cross-validation: Cross-validation is a technique used to evaluate the accuracy of a forecast model by testing it on a subset of the data that was not used in training the model.
Autocorrelation: Autocorrelation refers to the correlation between consecutive observations in a time series, which indicates the degree to which the data is self-similar over time.
Stationarity: Stationarity refers to the property of a time series where the statistical properties such as mean, variance, and autocorrelation remain constant over time.
ARIMA models: ARIMA models are a class of time series models that use autoregressive, integrated, and moving average components to model time series data.
Exogenous variables: Exogenous variables are external factors that affect the behavior of a time series, but are not part of the time series itself.
Kalman filtering: Kalman filtering is a technique used in time series analysis to update predictions based on new information, by calculating the optimal weighting between predicted and observed values.
Bayesian smoothing: Bayesian smoothing is a statistical method that estimates the posterior probability distribution of a time series based on historical data and prior knowledge, to produce a forecast.
Simple Exponential Smoothing: This method is used when there is no significant trend, and the data is stationary. In this method, the past data is given less weight as compared to the present data.
Double Exponential Smoothing: Also known as Holt's method, this technique is used when there is an upward or downward trend in data. The method takes into account the level and trend in data.
Triple Exponential Smoothing: Also called Holt-Winters' method, this technique includes both the trend and seasonality in data.
Seasonal Exponential Smoothing: This method extends the simple exponential smoothing to the seasonal time series. It includes seasonal factors that affect the seasonal patterns.
Holt-Winters' Seasonal Exponential Smoothing: This technique extends the Holt-Winters' method to include seasonality. Unlike the simple seasonal exponential smoothing, Holt-Winters' method can model both the trend and seasonality.
Brown's Exponential Smoothing: This method is used when there is a trend with some random variation. It includes damping and a rate parameter to manage the variations.
Croston's Method: This technique is used for intermittent demand data. It separates the demand signals from no-demand signals and generates forecasts.
ARIMAX: This method uses Autoregressive Integrated Moving Average (ARIMA) models to forecast time series along with other independent variables.
- "Exponential functions are used to assign exponentially decreasing weights over time."
- "It is an easily learned and easily applied procedure for making some determination based on prior assumptions by the user, such as seasonality."
- "Exponential smoothing is one of many window functions commonly applied to smooth data in signal processing, acting as low-pass filters to remove high-frequency noise."
- "This method is preceded by Poisson's use of recursive exponential window functions in convolutions from the 19th century, as well as Kolmogorov and Zurbenko's use of recursive moving averages from their studies of turbulence in the 1940s."
- "The raw data sequence is often represented by {x_t} beginning at time t = 0."
- "The output of the exponential smoothing algorithm is commonly written as {s_t}, 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 formulas: s_0 = x_0 and s_t = αx_t + (1-α)s_(t-1), t>0."
- "α is the smoothing factor, and 0<α<1."
- "Exponential smoothing is often used for analysis of time-series data."
- "Exponential smoothing acts as low-pass filters to remove high-frequency noise."
- "Exponential functions are used to assign exponentially decreasing weights over time."
- "It is an easily learned and easily applied procedure for making some determination based on prior assumptions."
- "Exponential smoothing is preceded by Poisson's use of recursive exponential window functions in convolutions from the 19th century and Kolmogorov and Zurbenko's use of recursive moving averages from their studies of turbulence in the 1940s."
- "Exponential smoothing is one of many window functions commonly applied to smooth data in signal processing, acting as low-pass filters to remove high-frequency noise."
- "The output of the exponential smoothing algorithm ({s_t}) may be regarded as a best estimate of what the next value of x will be."
- "Unlike the simple moving average, where the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time."
- "The smoothing factor (α) represents prior assumptions by the user and is typically chosen based on the specific application."
- "Exponential smoothing is an easily applied procedure for making determinations based on prior assumptions by the user, such as seasonality."
- "The smoothing factor (α) in exponential smoothing should be greater than 0 and less than 1."