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A consensus forecast is a prediction of the future created by combining several separate forecasts which have often been created using different methodologies. They are used in a number of sciences, ranging from econometrics to meteorology, and are also known as combining forecasts, forecast averaging or model averaging (in econometrics and statistics) and committee machines, ensemble ...
Exponential smoothing puts substantial weight on past observations, so the initial value of demand will have an unreasonably large effect on early forecasts. This problem can be overcome by allowing the process to evolve for a reasonable number of periods (10 or more) and using the average of the demand during those periods as the initial forecast.
Extension packages contain related and extended functionality: package tseries includes the function arma(), documented in "Fit ARMA Models to Time Series"; packagefracdiff contains fracdiff() for fractionally integrated ARMA processes; and package forecast includes auto.arima for selecting a parsimonious set of p, q.
For example, to calculate the 95% prediction interval for a normal distribution with a mean (μ) of 5 and a standard deviation (σ) of 1, then z is approximately 2. Therefore, the lower limit of the prediction interval is approximately 5 ‒ (2⋅1) = 3, and the upper limit is approximately 5 + (2⋅1) = 7, thus giving a prediction interval of ...
The ensemble forecast is usually evaluated by comparing the ensemble average of the individual forecasts for one forecast variable to the observed value of that variable (the "error"). This is combined with consideration of the degree of agreement between various forecasts within the ensemble system, as represented by their overall standard ...
Lottery mathematics is used to calculate probabilities of winning or losing a lottery game. It is based primarily on combinatorics, particularly the twelvefold way and combinations without replacement. It can also be used to analyze coincidences that happen in lottery drawings, such as repeated numbers appearing across different draws. [1
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In time series analysis used in statistics and econometrics, autoregressive integrated moving average (ARIMA) and seasonal ARIMA (SARIMA) models are generalizations of the autoregressive moving average (ARMA) model to non-stationary series and periodic variation, respectively.