MATH ASSIGNMENT

Math Assignment



Math Assignment

Answer 1

(a)

From the above graph, it can be observed that the data for the number of people employed is gradually increasing over the period. The number of people employed from 1970 to 1974 is increasing over the period; moreover, it is observed that in 1974, the number of people employed in retail trade industry was maximum.

(b)

A time series is a chronological sequence of observations on a particular variable. Usually the observations are taken at regular intervals (days, months, years), but the sampling could be irregular. Common examples of time series are the Dow Jones Industrial Average, Gross Domestic Product, unemployment rate, and airline passenger loads. A time series analysis consists of two steps: (1) building a model that represents a time series, and (2) using the model to predict (forecast) future values (Brillinger, 1975, 45).

If a time series has a regular pattern, then a value of the series should be a function of previous values. If Y is the target value that we are trying to model and predict, and Yt is the value of Y at time t, then the goal is to create a model of the form:

Yt = f(Yt-1, Yt-2, Yt-3, …, Yt-n) + et

Where Yt-1 is the value of Y for the previous observation, Yt-2 is the value two observations ago, etc., and et represents noise that does not follow a predictable pattern (this is called a random shock). Values of variables occurring prior to the current observation are called lag values. If a time series follows a repeating pattern, then the value of Yt is usually highly correlated with Yt-cycle where cycle is the number of observations in the regular cycle. For example, monthly observations with an annual cycle often can be modeled by

Yt = f(Yt-12)

The goal of building a time series model is the same as the goal for other types of predictive models which is to create a model such that the error between the predicted value of the target variable and the actual value is as small as possible (Wei, 1989, 96). The primary difference between time series models and other types of models is that lag values of the target variable are used as predictor variables, whereas traditional models use other variables as predictors, and the concept of a lag value doesn't apply because the observations don't represent a chronological sequence.

The time series model for this series that is “Trade” is mentioned below;

yt = xt B + Et; t = 1970, 1971, 1972, 1974

Moreover, the estimate of the components of your model is the beta value which will be based on the number of people employed in retail trade industry at that year.

(c)

Monthly forecasting of number of people employed in retail trade industry is as follow;

1975

Month 1

403.92

1975

Month 2

407.9592

1975

Month 3

440.5959

1975

Month 4

449.4079

1975

Month 5

458.396

1975

Month 6

504.2356

1975

Month 7

554.6592

1975

Month 8

610.1251

1975

Month 9

671.1376

1975

Month 10

738.2514

1975

Month 11

812.0765

1975

Month 12

893.2841

(d)

Limitations: Decomposition Method and Exponential Smoothing Method

As compared to the exponential smoothing method, the limitations of the decomposition method are important to ...