Time Series Analysis Quiz

<p>The power to which the variable is raised. (B)</p> Signup and view all the answers

<p>Square root transformation. (B)</p> Signup and view all the answers

<p>One or more reversals in curvature. (A)</p> Signup and view all the answers

<p>A random fluctuation and deviation from the average level. (B)</p> Signup and view all the answers

<p>Its slope remains constant over time. (B)</p> Signup and view all the answers

<p>The absence of long-run growth or decline. (A)</p> Signup and view all the answers

<p>yt = β0 + β1t + β2t^2 (D)</p> Signup and view all the answers

<p>It must be independent and satisfy constant variance. (A)</p> Signup and view all the answers

<p>Indicates multiple changes in the direction of the data. (D)</p> Signup and view all the answers

<p>To plan the operations of its fish processing plant effectively. (C)</p> Signup and view all the answers

<p>The independence of residuals (D)</p> Signup and view all the answers

<p>1.70 (C)</p> Signup and view all the answers

<p>A discernible pattern in the spread of points (A)</p> Signup and view all the answers

<p>0.90 (D)</p> Signup and view all the answers

<p>4 (A)</p> Signup and view all the answers

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

<p>The model has positive autocorrelation (B)</p> Signup and view all the answers

<p>Residuals must have constant variance (D)</p> Signup and view all the answers

<p>Decision is inconclusive (A)</p> Signup and view all the answers

<p>The error terms are not autocorrelated (D)</p> Signup and view all the answers

<p>No apparent pattern in residuals (A)</p> Signup and view all the answers

<p>If (4 - d) is less than dL,α (A)</p> Signup and view all the answers

<p>Reject H0 (C)</p> Signup and view all the answers

<p>The degree of autocorrelation in residuals (A)</p> Signup and view all the answers

<p>No evidence of autocorrelation (A)</p> Signup and view all the answers

<p>The test is inclusive (D)</p> Signup and view all the answers

<p>The error terms are positively or negatively autocorrelated (B)</p> Signup and view all the answers

<p>yˆt = 198.02899 + 8.07435t (B)</p> Signup and view all the answers

<p>To balance demand fulfillment and minimize excess inventory (C)</p> Signup and view all the answers

<p>Future sales of the Bismark X-12 calculators (D)</p> Signup and view all the answers

<p>β1 (C)</p> Signup and view all the answers

<p>Using the linear regression equation derived from historical data (B)</p> Signup and view all the answers

<p>The range within which the forecasted sales are expected to fall (D)</p> Signup and view all the answers

<p>8.07435 (C)</p> Signup and view all the answers

<p>The initial sales value when time is zero (B)</p> Signup and view all the answers

<p>Current stock levels (C)</p> Signup and view all the answers

<p>Variances and t-values from sample data (B)</p> Signup and view all the answers

<p>Sales are likely to continue rising if past trends hold (A)</p> Signup and view all the answers

<p>The data exhibits exponential growth. (A)</p> Signup and view all the answers

<p>α0 = 2.07012, α1 = 0.25688 (C)</p> Signup and view all the answers

<p>100 * (β1 − 1) (B)</p> Signup and view all the answers

<p>It provides a range within which the actual value of y16 is expected to fall. (B)</p> Signup and view all the answers

<p>The error terms are independent or not autocorrelated. (A)</p> Signup and view all the answers

<p>483.09 (C)</p> Signup and view all the answers

<p>Higher values suggest a better fit of the model to the data. (A)</p> Signup and view all the answers

<p>It ensures lower MSE is obtained from testing data. (B)</p> Signup and view all the answers

A statistical model that relates a dependent variable to time and accounts for time-related patterns. It is used when the underlying relationships stay consistent over time.

A line or curve that represents the long-term increase or decrease in a time series.

A time series model where the trend is represented by a straight line. It assumes a constant rate of change in the variable over time.

A time series model where the trend is represented by a curved line. It shows a changing rate of growth or decline over time.

A time series model where the trend is represented by a polynomial equation of higher order (more than 2). It allows for complex trends with reversals in curvature.

The deviation between the actual value of a time series and its average level at a specific point in time.

The assumption that the variance (spread) of the error term in a time series model remains constant over time.

The assumption that the error terms in a time series model are independent of each other, implying that past errors don't influence future errors.

A statistical method used to predict future demand for a product, especially when the demand shows an upward trend.

A line representing the relationship between time and demand, used to predict future values. It shows the expected trend and allows us to forecast future demand.

A statistical measure indicating the slope of the trend line. It represents the rate of change in demand per unit of time, for example, demand increase per month.

A statistical measure representing the point where the trend line intersects the Y-axis. It gives the starting point of demand at the beginning of the time period.

A point estimate of demand obtained by plugging a specific time value into the regression equation.

A range of values within which the actual demand is expected to fall with a certain level of confidence.

The standard error of the regression estimate, reflecting the variability of the data around the trend line.

The number of data points used in the regression analysis, which influences the precision of the prediction interval.

The chosen level of confidence for the prediction interval, typically set at 95% or 99%.

The time period in the future for which we want to predict the demand.

A statistical test that examines the relationship between consecutive error terms in a time series regression model, specifically looking for patterns in the residuals.

A situation where the error terms in a time series regression model are positively correlated, meaning that a positive error in one period tends to be followed by another positive error in the subsequent period.

A situation where the error terms in a time series regression model are negatively correlated, meaning that a positive error in one period tends to be followed by a negative error in the subsequent period.

The null hypothesis in the Durbin-Watson test, stating that there is no autocorrelation present in the error terms of the regression model.

The alternative hypothesis in the Durbin-Watson test, stating that there is negative autocorrelation present in the error terms of the regression model.

The alternative hypothesis in the Durbin-Watson test, stating that there is positive or negative autocorrelation present in the error terms of the regression model.

A value calculated using the Durbin-Watson test to assess the presence of autocorrelation in the error terms. It ranges between 0 and 4.

A critical value used in the Durbin-Watson test to determine the significance of the calculated Durbin-Watson statistic, helping to decide whether or not to reject the null hypothesis.

A statistical test used to detect autocorrelation in the residuals of a regression model. It measures whether consecutive error terms in a time series are correlated.

A value obtained from the Durbin-Watson statistic. It falls between 0 and 4, with values closer to 2 indicating no autocorrelation.

The lower bound of the Durbin-Watson test statistic, below which there is evidence of positive autocorrelation.

The upper bound of the Durbin-Watson test statistic, above which there is evidence of negative autocorrelation.

The number of independent variables in the regression model. It affects the critical values of the Durbin-Watson test.

The number of observations in the time series. It affects the critical values of the Durbin-Watson test.

A situation where the error terms in a regression model are correlated over time, meaning past errors influence future errors.

A condition where the variance of the error terms in a regression model is not constant over time. It means errors have uneven spread.

In the Durbin-Watson test, we examine the residuals (the differences between the predicted and actual values) of a regression model to detect autocorrelation.

A plot of the residuals against the fitted values (predicted values from the regression model) to visually inspect for patterns that might indicate autocorrelation or heteroscedasticity.

The magnitude of seasonal swings does not depend on the level of the time series. Think of it like a consistent pattern, regardless of the overall trend.

The magnitude of seasonal swings changes with the overall level of the time series. Think of it as a pattern that grows or shrinks with the overall trend.

A technique used to transform data to make seasonal patterns more consistent. This usually involves taking a power or logarithm of the original values.

Used to produce a time series with a constant seasonal variation. Typically involves raising the original data to a power between 0 and 1.

Common transformations include square root, quartic root, and natural logarithm. Each transformation has specific properties that can be used depending on the nature of the seasonal pattern.

A statistical model that describes the relationship between a dependent variable and time, where the growth is exponential.

The process of transforming an exponential growth model into a linear model by taking the natural logarithm of both sides.

The estimated growth rate calculated from the transformed model using the exponential function.

A statistical measure of the variation of the data points around the regression line, indicating the goodness of fit for the model.

A statistical measure comparing the goodness of fit of different models, with higher values indicating a better fit to the data.