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<p>Roots of θ(z)=0 must be greater than one in absolute value. (C)</p> Signup and view all the answers

<p>E(yt) = μ / (1 - φ1 - φ2 - ... - φp) (C)</p> Signup and view all the answers

<p>It exhibits a geometrically decaying pattern. (C)</p> Signup and view all the answers

<p>It displays a geometrically decaying pattern. (A)</p> Signup and view all the answers

<p>It has a number of spikes equal to the MA order. (C)</p> Signup and view all the answers

<p>They are prone to breakdown around turning points. (C)</p> Signup and view all the answers

<p>Illusory patterns (D)</p> Signup and view all the answers

<p>Combine statistical models with expert judgement. (A)</p> Signup and view all the answers

<p>It usually declines with the forecasting horizon. (C)</p> Signup and view all the answers

<p>Statistical models cannot account for complex patterns. (C)</p> Signup and view all the answers

<p>$\frac{\Phi_1^s \sigma^2}{(1 - \Phi_1^2)}$ (B)</p> Signup and view all the answers

<p>1 (C)</p> Signup and view all the answers

<p>1 (D)</p> Signup and view all the answers

<p>It measures correlations after removing the effects of intermediate lags. (A)</p> Signup and view all the answers

<p>$\Phi_1^s$ (D)</p> Signup and view all the answers

<p>$\frac{\tau_2 - \tau_{12}}{(1 - \tau_{12})}$ (D)</p> Signup and view all the answers

<p>$\Phi_1$ (B)</p> Signup and view all the answers

<p>Partial Autocorrelation Function (A)</p> Signup and view all the answers

<p>To choose the number of parameters that minimizes the criterion (C)</p> Signup and view all the answers

<p>AIC will often choose 'bigger' models than SBIC (A)</p> Signup and view all the answers

<p>It involves differencing the original variable (C)</p> Signup and view all the answers

<p>It could help identify the limitations of a model (C)</p> Signup and view all the answers

<p>A preference for simpler models (C)</p> Signup and view all the answers

<p>ARMA models are a subset of ARIMA models (B)</p> Signup and view all the answers

<p>A model that balances fit with the number of parameters (B)</p> Signup and view all the answers

<p>Shape of the data distribution (D)</p> Signup and view all the answers

<p>It is very simple to use. (B)</p> Signup and view all the answers

<p>Econometric forecasting relies on structural models. (A)</p> Signup and view all the answers

<p>It provides a good test of the model's predictive capability. (A)</p> Signup and view all the answers

<p>The conditional expectation of yt+1 given the past information. (D)</p> Signup and view all the answers

<p>There is no predictable pattern for future values. (A)</p> Signup and view all the answers

<p>y is influenced by a linear combination of predictors and an error term. (B)</p> Signup and view all the answers

<p>It suggests that future values are likely to remain the same as the last observed value. (D)</p> Signup and view all the answers

<p>It indicates forecasts depend on expected values of predictors. (B)</p> Signup and view all the answers

<p>The autocorrelation at lag 1 (B)</p> Signup and view all the answers

<p>$ heta_1 = -0.5$, $ heta_2 = 0.25$ (A)</p> Signup and view all the answers

<p>It equals 0 (D)</p> Signup and view all the answers

<p>Variance of the process (B)</p> Signup and view all the answers

<p>$ heta_2 rac{ au_0}{(1 + heta_1^2 + heta_2^2)}$ (D)</p> Signup and view all the answers

<p>$( heta_1 + heta_1 heta_2) au_0$ (B)</p> Signup and view all the answers

<p>A model that includes past observations of itself (B)</p> Signup and view all the answers

<p>0 (A)</p> Signup and view all the answers

The covariance between a time series variable and a lagged version of itself.

The normalized autocovariance, indicating the strength of the linear relationship between lagged values in a time series.

An autoregressive model of order p, describing a time series using past values of itself.

A graphical representation of autocorrelations for a time series, showing the correlation with lagged values.

Models that predict future values of a variable based on its past values.

The covariance between a time series variable and its first lagged value.

The covariance between a time series variable and its second lagged value.

Autocovariances for lags greater than 2 are zero.

The covariance between an observation and a lagged version of itself.

Autocovariance divided by variance; measures correlation.

Correlation between lagged observation, removing intermediate lags effect.

Autoregressive model; current observation depends on p previous values.

Autoregressive Moving Average model with p autoregressive and q moving average terms.

Time difference between two observations in a time series.

PACF helpful for distinguishing AR vs. ARMA processes.

Correlation between current observation and preceding observation

The process of evaluating the adequacy of a fitted ARMA model to ensure it accurately represents the time series data.

A method for model checking where you intentionally overfit the model to identify potential issues and find the optimal model.

Analyzing the residuals from a fitted ARMA model to assess the model's ability to capture the data's underlying patterns.

A model that uses the fewest possible parameters while still adequately explaining the data.

A statistical measure used to compare different ARMA models by balancing the model's goodness of fit with the complexity of the model

Akaike Information Criterion, a measure that penalizes model complexity, favoring simpler models with good fit.

Schwarz Bayesian Information Criterion, a measure that places a stronger penalty on model complexity than AIC, favoring even simpler models.

Hannan-Quinn Information Criterion, a measure that penalizes model complexity in between AIC and SBIC.

The partial autocorrelation function (PACF) of an AR(p) process is zero after lag p. This means that there are no direct connections between yt and its past values beyond lag p.

The PACF of an MA(q) process decays geometrically. This is because there are direct connections between yt and all its past values, although these connections weaken as the lag increases.

An ARMA(p,q) model combines the characteristics of an autoregressive (AR) model of order p and a moving average (MA) model of order q. It uses both past values of the time series and past error terms to predict future values.

For an MA(q) process to be invertible, the roots of the MA polynomial (z)=0 must be greater than one in absolute value. This ensures that the MA part of the model can be represented as an infinite AR process.

The mean of an ARMA series is calculated by dividing  (the constant term) by 1 − 1 − 2 −...−p, where 1, 2, ... p are the AR coefficients.

The autocorrelation function (ACF) of an ARMA process displays a combination of patterns from its AR and MA components. For lags beyond q, the behavior becomes identical to the individual AR(p) model.

The autocorrelation function (ACF) of an AR(p) model decays geometrically.

The autocorrelation function (ACF) of an MA(q) model has a finite number of spikes, equal to the order of the MA model (q).

Forecasting is making predictions about future values based on past data.

The two main forecasting approaches are econometric (structural) forecasting and time series forecasting.

In-sample forecasting uses the same data for model building and evaluation, while out-of-sample forecasting uses a separate dataset for evaluation.

A multi-step ahead forecast predicts a future value multiple time steps ahead.

A recursive forecasting window uses all available data up to the forecast point to predict future values.

A rolling window uses a fixed window of past data to predict future values, moving the window forward in time.

The expected value of a variable given information up to a specific time.

No, we cannot forecast a white noise process because its future values are completely unpredictable.

Separating meaningful patterns (signal) from random fluctuations (noise) in data.

Challenges in extracting meaningful insights from large datasets, including overfitting, irrelevant features, and data quality.

Balancing model simplicity (easier to interpret, less prone to overfitting) with complexity (potentially higher accuracy).

Forecasting models have inherent limitations: they are extrapolative (predicting based on past patterns), prone to break down at turning points, and often lose accuracy over time.

Combining statistical models with expert opinion can improve forecasts, but expert judgment can be biased (overconfidence, recency bias, etc.)