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Examoogle • User • info@examoogle.com • EE-2024-8821
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The n-th order auto-regressive model of sequence d s σ can be expressed as
∑ i = 1 n a i d s ( σ - i ) + w σ
∑ i = 1 n a i d s ( σ - i ) - w σ
∑ i = 1 n a i d s ( σ ) - w σ
None of above
∑i=1naids(σ-i)+wσ
Quick Summary: An n-th order auto-regressive (AR(n)) model represents the current value of a time series, $d_s(\sigma)$, as a linear weighted combination of its previous $n$ values, plus a random noise or white noise term, $w(\sigma)$. The coefficients $a_i$ represent the weights assigned to the historical data points at lags $i=1, 2, ..., n$.
An n-th order auto-regressive (AR(n)) model represents the current value of a time series, ds(σ), as a linear weighted combination of its previous n values, plus a random noise or white noise term, w(σ). The coefficients ai represent the weights assigned to the historical data points at lags i=1,2,...,n.
ds(σ)=∑i=1naids(σ−i)+w(σ) — Standard AR(n) model equation
In time series analysis and load forecasting, the AR model assumes that the future state depends linearly on past states. The term ∑i=1naids(σ−i) computes the deterministic linear trend based on the history, while w(σ) accounts for the stochastic, unpredictable component of the system.
The order 'n' defines the number of past observations included in the model.
AR models are fundamental in stochastic process modeling and short-term load forecasting.
The white noise term w(σ) is typically assumed to have zero mean and constant variance (stationary).
Model stability requires the roots of the characteristic equation to lie within the unit circle.
Simple to implement for linear forecasting problems.
Effective for stationary time series data.
Does not handle non-stationary trends well without differencing (ARIMA).
Sensitive to the selection of model order 'n'.
Short-term electricity load forecasting.
Signal processing and spectrum estimation.
Economic and financial time series analysis.
The AR model is a subset of the broader ARMA (Auto-Regressive Moving Average) family.
Option B is incorrect because the noise term should be additive in standard definitions to account for fluctuations.
Option C is incorrect as it implies the current value is a function of the current demand directly, which contradicts the 'auto-regressive' (lagged) property.
A is correct — The n-th order AR model defines the current state as a linear combination of its n previous states and an additive white noise term.
Always verify the lag indices in AR models; AR models specifically depend on previous time steps (σ−i), whereas static regressions depend on the current time step (σ).