Exam 12: Time Series Analysis and Forecasting

The random walk model is written as: $Y _ { t } = Y _ { t - 1 } + m + e _ { t }$ )In this model, $e _ { t }$ Represents the:

The cyclic component of a time series is more likely to exhibit business cycles that record periods of economic recession and inflation.

Related to the runs test,if T is reasonably large (T > 20 is suggested),then the statistic can be used to perform this test.

The idea behind the runs test is that a random number series should have a number of runs that is:

In a random walk model,there are significantly more runs than expected,and the autocorrelations are not significant.

The null hypothesis in a runs test is $H _ { 0 }$ the data series is random

The smoothing constant used in simple exponential smoothing is analogous to the span in moving averages.

Which of the following summary measures for forecast errors does not depend on the units of the forecast variable?

Suppose that a simple exponential smoothing model is used (with $a$ = 0.40)to forecast monthly sandwich sales at a local sandwich shop.The forecasted demand for September was 1560 and the actual demand was 1480 sandwiches.Given this information,what would be the forecast number of sandwiches for October?

Examples of non-random patterns that may be evident on a time series graph include:

To deseasonalize an observation (assuming a multiplicative model of seasonality),multiply it by the appropriate seasonal index.

Regression models with seasonal dummy variables produce coefficients for each quarter,which represent the additive or multiplicative factors relative to the annual average.

The runs test is a formal test of the null hypothesis of randomness.If there are too many or too few runs in the series,then we conclude that the series is not random.

In a random series,successive observations are probabilistically independent of one another.If this property is violated,the observations are said to be:

A moving average is the average of the observations in the past few periods,where the number of terms in the average is the span.

An equation for the random walk model is given by the equation: $D Y _ { t } = \mu + \varepsilon _ { t }$ ,where $D Y _ { t }$ is the change in the time series from time t to time t - 1, $\mu$ is a constant,and $\varepsilon _ { t }$ is a random variable (noise)with mean 0 and some standard deviation $\sigma$ .

We compute the five-period moving averages for all time periods except the first two.

When using the moving average method,you must select which represent(s)the number of terms in the moving average.

Holt's method is an exponential smoothing method,which is appropriate for a series with seasonality and possibly a trend.

The linear trend $\hat { Y } _ { t } = 120 + 2 _ { t }$ Was estimated using a time series with 20 time periods.The forecasted value for time period 21 is