Question 1

An exponential trend can have a turning point (peak or trough).

Accepted Answer

An exponential trend is characterized by a consistent multiplicative rate of change and does not have turning points like peaks or troughs; it either increases or decreases continuously.

Question 2

Multiplicative models are avoided in business because they are too complicated.

Accepted Answer

Multiplicative models are not avoided in business because they are too complicated. In fact, they are often used in areas such as forecasting, pricing, and risk management. However, they may require more complex calculations and data analysis than additive models, which could lead some businesses to prefer the latter.

Question 3

Multiplicative models are most appropriate over longer periods of time or when the data magnitude is growing rapidly over time.

Accepted Answer

Multiplicative models are better suited for situations where the data's magnitude is changing significantly over time. These models are particularly useful over longer periods of time, where trends may be more pronounced and data is subject to more variability. Multiplicative models allow for changes in variability over time and can capture more complex relationships between variables. However, for short-term data or when the data is relatively stable, additive models may be more appropriate.

Question 4

Additive models are most appropriate over longer periods of time or when the data magnitude is growing rapidly over time.

Accepted Answer

Additive models are best when the seasonal variations are roughly constant over time, whereas multiplicative models are more appropriate when the seasonal variations increase or decrease proportionally with the level of the data.

Question 5

The shape of the fitted quadratic model y_t = 544 + 62t - 3.2t² is declining, then rising.

Accepted Answer

The shape of the fitted quadratic model is determined by the coefficient of the $t^2$ term. Since the coefficient is -3.2, which is negative, the shape of the model is a downward-opening parabola, indicating it rises first and then declines.

Question 6

Over the short run, exponential and linear trends may look alike.

Accepted Answer

Exponential and linear trends may look similar in the short run because they both increase or decrease steadily. However, over the long run, the exponential trend will grow at an increasing rate, while the linear trend will grow at a constant rate.

Question 7

The shape of the fitted quadratic model y_t = 823 + 72t - 5.1t² is rising, then declining.

Accepted Answer

The quadratic model has a coefficient of -5.1 for the t squared term, indicating a parabolic shape. Since the coefficient is negative, the curve is opening downward, meaning it first rises to a peak and then declines. Therefore, the statement is true.

Question 8

The shape of the fitted quadratic model y_t = 324 - 42t - 1.3t² is declining, then rising.

Accepted Answer

The given quadratic model is $y = 324 - 42t - 1.3t^2$. The coefficient of $t^2$ is negative (-1.3), indicating that the parabola opens downwards, meaning it rises first and then declines.

Question 9

Exponential smoothing and moving averages are especially useful for data with a clear trend.

Accepted Answer

Exponential smoothing and moving averages are more suited for data that does not display a clear trend or seasonal patterns, as they primarily smooth out short-term fluctuations to help identify the overall level in the data.

Question 10

The linear model's R² may exceed the quadratic model's R² fitted to the same data.

Accepted Answer

The answer of The linear model's R² may exceed the...

Question 11

An exponential trend allows growth but cannot be used if the time series is declining.

Accepted Answer

An exponential trend can model both growth and decline, as it reflects a constant percentage change over time, which can be positive (growth) or negative (decline).

Question 12

Moving average models are causal models (as opposed to time-series models).

Accepted Answer

Moving average models are a type of time-series model, specifically designed to smooth out short-term fluctuations and highlight longer-term trends or cycles. They are not causal models, which would imply a direct cause-and-effect relationship.

Question 13

A firm's balance sheet contains data measured over a period of time, as opposed to being measured at a point in time.

Accepted Answer

A firm's balance sheet presents data at a specific point in time, usually at the end of an accounting period. It provides a snapshot of the company's financial position at that moment.

Question 14

The shape of the fitted exponential model y_t = 256e^-.07^t is always declining.

Accepted Answer

The exponential model equation includes a negative exponent (-0.07) on the variable t, indicating that the exponential function is decreasing over time. Therefore, the shape of the fitted model is always declining.

Question 15

A firm's income statement contains data measured over a period of time, as opposed to being measured at a point in time.

Accepted Answer

An income statement, also known as a profit and loss statement, shows a company's revenues, expenses, and net income or loss over a specified period of time, such as a month, quarter, or year. It is therefore a measure of performance over a period of time, rather than a single point in time.

Question 16

The quadratic model can never have more than one turning point (peaks or troughs).

Accepted Answer

The quadratic function is a second-degree polynomial function, and always has exactly one turning point. The turning point is either a maximum (for a function with a negative leading coefficient), or a minimum (for a function with a positive leading coefficient).

Question 17

The quadratic model's R² is always at least as high as the linear model fitted to the same data.

Accepted Answer

This statement is true because a quadratic model involves a squared term, which can lead to a better fit of the data compared to a linear model. This usually results in a higher R² value for the quadratic model.

Question 18

Cycles are usually ignored because there is no general theory to describe them.

Accepted Answer

Cycles are not ignored because there is no general theory to describe them. In fact, there are several general theories that can be used to describe cycles, such as the theory of dynamical systems and the theory of graphs.

Question 19

A multiplicative time-series model Y = T × C × S × I becomes an additive model if we take the logarithm of each side of the equation.

Accepted Answer

Taking the logarithm of both sides of a multiplicative time-series model $Y = T \times C \times S \times I$ converts it into an additive model because the logarithm of a product is equal to the sum of the logarithms ($\log(AB) = \log(A) + \log(B)$). Thus, $\log(Y) = \log(T) + \log(C) + \log(S) + \log(I)$.

Question 20

Seasonality is usually ignored because there is no statistical way to describe it.

Accepted Answer

Seasonality can be described using various statistical tools such as time series analysis, seasonal index, and seasonal decomposition. Therefore, it is incorrect to say that seasonality is usually ignored because there is no statistical way to describe it.

Quiz 14: Time Series Analysis