Page 42 - Industrial Process Plant Construction Estimating and Man Hour Analysis

12 Industrial process plant construction estimating and man-hour analysis

1.6 Time series
Time series is a set of observations taken at specified times, usually at equal
intervals, and is defined by the values Y1, Y2, … of a variable Y at times t1,
t2, …. Thus, Y is a function of t, Y¼F(t). The analysis of time series consists
of a mathematical description of component movements. Analysis of move-
ments is of great value in many connections to construction, one of which is
the problem of forecasting future movements. Thus, the statistical techniques
used in forecasting time series can be used to uncover the relationships that exist
in construction.

1.6.1 Simple moving average
Given a set of numbers

Y 1 ,Y 2 ,…
define a moving average of order m to be given by the sequence of arithmetic
means:

Y1þY2þ⋯þMy=m,Y2þY3þ⋯þym=m,Y3þY4þ⋯þmy=m,…
The sums in the numerators are moving totals of order m.
Data given annually or monthly, a moving average of order m is called
respectively an m year average or m month average.
Moving averages have the property to reduce the amount of variation pre-
sent in the data. In the case of time series, this property is used to eliminate fluc-
tuations, and the process is called smoothing of time series.
Using a simple moving average model, forecast the next value(s) in a time
series based on the average of a fixed finite number m of the previous values.
Thus, for all i>m,

^ yi ¼ 1=m Σyi ¼ yi mþ⋯þyi 1ð Þ=m

1.6.2 Excel functions
AVERAGE (number 1, number 2): returns the average (arithmetic mean)
of its arguments, which can be numbers or names, arrays, or references that
contain numbers.
ABS (number): returns the absolute value of a number, a number without
its sign.

Using Excel statistical functions set up Table 1.6.1
To use the Excel statistical functions, go to quick access toolbar, select more
functions, and then, select statistical.