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Examoogle • User • info@examoogle.com • EE-2024-8821
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Which of the following is the simplest form of stochastic time series model?
Generalize load modelling
Estimation of periodic components
Time Estimation
Auto-regressive model
Auto-regressive model
Quick Summary: The Auto-regressive (AR) model is considered the simplest form of stochastic time series model because it represents the current value of a time series as a linear combination of its previous values plus a white noise term. It is widely used in short-term load forecasting for its computational simplicity and mathematical tractability.
The Auto-regressive (AR) model is considered the simplest form of stochastic time series model because it represents the current value of a time series as a linear combination of its previous values plus a white noise term. It is widely used in short-term load forecasting for its computational simplicity and mathematical tractability.
Yt=∑i=1pϕiYt−i+ϵt — The general expression for an AR(p) model where ϕ are coefficients.
The principle relies on the assumption that future values are dependent on past observations. An AR(p) model of order 'p' relates the current observation Yt to p previous observations Yt−1,Yt−2,...,Yt−p and an error term ϵt. The weights of these past values are estimated using techniques such as Yule-Walker equations or Least Squares.
AR models are linear models where past values predict future outcomes.
The parameter 'p' denotes the number of lags included in the model.
Stationarity is a key requirement for the stability of the model.
They are foundational to the more complex ARMA and ARIMA models.
Low computational overhead
Easy to interpret parameters
Effective for short-term stationary time series data
Ineffective for long-term trends without differencing
Sensitive to outliers in training data
Cannot capture complex non-linear relationships alone
Short-term electrical load forecasting
Signal processing
Financial time series analysis
AR models assume that the process is stationary, meaning its statistical properties like mean and variance remain constant over time.
Option B (Estimation of periodic components) is typically handled via Fourier Analysis or seasonal decomposition, not specifically a 'stochastic model'.
D is correct — The Auto-regressive (AR) model is the simplest stochastic time series model as it expresses the current value as a linear function of its own preceding values.
In competitive exams, remember that if the model requires past errors as well as past values, it evolves into an ARMA (Auto-Regressive Moving Average) model.