Linear Algebra Fundamentals Quiz

A time series where the value at any given time is equal to the previous value plus a random shock. It's essentially a series of random steps, where each step is independent of the previous ones.

A random walk where the process's average value does not change over time. This means the series has no tendency to drift upward or downward.

A random walk where the process's average value changes steadily over time. The series has a consistent drift to either higher or lower values.

A statistical concept implying that market prices are inherently unpredictable, making it impossible to consistently profit from market trends.

The value of the time series at a given time (t) depends solely on the value at the previous time (t-1) and a random shock. It lacks memory or any influence from past values.

The variance of the time series grows indefinitely over time. This means the series becomes increasingly volatile.

The initial starting value of the time series. This is typically set to zero in practical applications.

A statistical model where random shocks do not dissipate over time. The impact of a shock is permanent and continues to influence the series.

The variance of the predicted mean, indicating the spread of possible mean predictions.

The variance of a single prediction, representing the spread of possible values for a particular observation.

A concise way to represent the relationship between multiple variables using matrices.

A statistical measure that quantifies the variability of the data points around a regression line.

A matrix that provides the variances and covariances of the estimated coefficients in a regression model.

The standard deviation of an estimated coefficient, indicating the degree of uncertainty associated with it.

An approach to regression analysis using matrix algebra, offering succinct and efficient representation of the relationships between variables.

The process of estimating unknown parameters in a statistical model using observed data.

A matrix obtained by interchanging rows and columns of the original matrix. Think of it as flipping the matrix across its diagonal.

A matrix with the same number of rows and columns.

A square matrix with non-zero elements only on the main diagonal (top-left to bottom-right). All other elements are zero.

A diagonal matrix where all the diagonal elements are equal.

A special diagonal matrix with all diagonal elements equal to 1.

A square matrix where the elements above the main diagonal are mirrored by the elements below the main diagonal.

A matrix obtained by deleting rows and columns from the original matrix.

A smaller matrix created by removing rows and columns from a larger matrix.

When two non-stationary time series variables have a long-term, stable relationship, even though they are individually fluctuating, they are considered cointegrated.

A statistical test used to determine if a regression between time series variables is spurious or meaningful. It verifies if the residuals (errors) from the regression are stationary.

A statistical test that examines the residuals (errors) from a regression, using the Dickey-Fuller (DF) or Augmented Dickey-Fuller (ADF) test for stationarity. If the residuals are stationary, the regression is considered cointegrated.

The difference between the actual value of a variable and its predicted value based on a regression model. They represent the errors or discrepancies in the model's predictions.

A time series variable is stationary if its statistical properties (mean, variance) remain constant over time. It does not have a trend or seasonal patterns.

A time series variable that has a trend or pattern that persists over time. It does not have a constant mean or variance.

A type of regression where the relationship between independent and dependent variables is spurious, meaning it is not a real or meaningful relationship. Typically occurs with non-stationary time series.

The statistical properties of a series, such as mean, variance, and autocorrelation, do not change over time. It signifies a lack of trend or seasonal patterns.

A statistical test used to determine if two time series are cointegrated. It examines the residuals from a regression of one series on another to see if they are stationary.

The value of the test statistic in the Engle-Granger test that separates the rejection region from the non-rejection region. It is used to determine if the null hypothesis of no cointegration should be rejected.

A statistical model that explains how a time series adjusts to deviations from its long-term equilibrium relationship with another time series. It incorporates the error term from the cointegrating regression.

The difference between the actual value of a time series and its equilibrium value, as determined by the cointegrating regression. It represents the disequilibrium in the relationship between the two time series.

A mathematical theorem stating that if two time series are cointegrated, their relationship can be expressed as an Error Correction Model (ECM). It provides a framework for modeling the relationship between cointegrated time series.

A statistical model describing the short-term dynamics of a time series. It includes past values of the series, the error term, and variables determining the long-term equilibrium.

The process of returning to the long-term equilibrium relationship after a short-term deviation. It involves adjustments driven by the error term, ensuring the time series eventually aligns with its long-term path.

The parameter determining the speed of adjustment to the long-term equilibrium. A larger absolute value implies a faster convergence to equilibrium.

A statistical test used to determine if a time series is stationary or has a unit root. The null hypothesis of the DF test is that the time series has a unit root, meaning it is non-stationary. Rejecting the null hypothesis implies the process is stationary.

A modification of the DF test designed to address the issue of serial correlation in the error terms. It involves adding lagged difference terms of the dependent variable to the regression equation.

The null hypothesis of the DF/ADF test for whether a time series is stationary around a deterministic trend. It means the time series has a unit root and is non-stationary around the trend.

A statistical test used to determine if multiple coefficients in a regression model are jointly zero. It involves comparing the unrestricted model with the restricted model where the coefficients are constrained to be zero.

A test for unit roots that addresses the assumption of independently and identically distributed (i.i.d) error terms in the DF test. It adjusts the DF statistic to account for potential serial correlation.

In the context of the DF test, this refers to a time series that has a unit root, meaning it's non-stationary. It's crucial to know that critical values for the test are different for each type of non-stationary process (zero mean, nonzero mean, or deterministic trend).

A time series that has a unit root and is non-stationary around a deterministic trend. This means that the time series exhibits a trend but also fluctuates randomly around that trend.

A time series that exhibits a trend but also fluctuates randomly around that trend. The trend is deterministic in this case, which means it can be described by a mathematical function.