Time Series Analyze

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Time Series Analyze
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Forecasting

• Almost all managerial decisions are based on
  forecast. Every decision becomes effective at
  some point in the future, so it should be based
  on forecasts of future conditions.
• Forecasts are needed throughout an organization
• Neither is forecasting ever "finished".

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Statistical Forecasting

• The selection and implementation of the proper
  forecast methodology has always been an important
  planning and control issue for most firms and
  agencies.
• There are two main approaches to forecasting.
• Either the estimate of future value is based on
  an analysis of factors which are believed to
  influence future values (the explanatory method)
• or else the prediction is based on an inferred
  study of past general data behavior over time
  (the extrapolation method).

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Forecasting inputs

• These come from the decision maker's environment,
  they are Time Series Data
• Time Series Models are one class of the
  Forecasting Technques.

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Major Elements of Time Series Models

• Use of repeated measurements
• Variability is assessed across time
• Independent and dependent variables are carefully
  specified while other variables are held constant
• Employ a flexible format

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Important Parameters of Time Series Data

• Slope (Trend)
• Variability

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Methods for Handling Instability

• Analyze sources of variability
• Wait for a more stable pattern to emerge
• Examine the temporal unit of analysis

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Baseline Trends
Examples of Baselines
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Unstable
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Index numbers
Basis index divisor is absolute, the base
dataChain index disvisor is relativ, the
previous data
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The average development
The geometrical mean.
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Correlation Regression
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Related Measures
With any set of items (for example the population
of 9 persons we have discussed elsewhere) we
could, if we chose to, measure more than one
feature, We could, for example, measure each
persons weight as well as their height. The
population of paired numbers would be described
as related measures provided that we always knew
which weight was related to which height. That
is, we always associated the weight of a given
person with that same person's height
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Correlation
Given a pair of related measures (X and Y) on
each of a set of items, the correlation
coefficient (r) provides an index of the degree
to which the paired measures co-vary in a linear
fashion. In general r will be positive when items
with large values of X also tend to have large
values of Y whereas items with small values of X
tend to have small values of Y. Correspondingly,
r will be negative when Items with large values
of X tend to have small values of Y whereas items
with small values of X tend to have large values
of Y.
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The calculation of the correlation coefficien
1. The covariance Returns covariance, the
average of the products of deviations for each
data point pair. Use covariance to determine the
relationship between two data sets.
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The equation for the correlation coefficient is
and
Is the standard deviation of X
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Numerically, r can assume any value between -1
and 1 depending upon the degree of the
relationship. Plus and minus one indicate perfect
positive and negative relationships whereas zero
indicates that the X and Y values do not co-vary
in any linear fashion.
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Regression

• Given a pair of related measures ( X and Y ) on
  each of a set of items, the term "regression" is
  used to characterize the manner in which one of
  the measures (for example the Y measures) change
  as the other measure ( in this case, the X
  measure) changes.
• For any set of related measures, it is possible
  to specify a line that approximates the mean of
  the Y measures for those items with a given X
  measure.
• By revealing how the mean of the Y measures
  change as the various X measures change, this
  line is understood to describe the regression of
  Y on X.

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It is noteworthy that for the same set of related
measures there is always a second regression line
that describes the regression of X on Y. The
regression line is the predicted value of Y for
each value of X.
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The calculation of the parameters of the
regression line. ( In Excel)
LINEST
Calculates the statistics for a line by using the
"least squares" method to calculate a straight
line that best fits your data, and returns an
array that describes the line. Because this
function returns an array of values, it must be
entered as an array formula. The equation for the
line is y mx b where the dependent y-value
is a function of the independent x-values.
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In this case (ymxb)
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Statistical functions in Excel
 AVERDEV Returns the average of the absolute
deviations of data points from their
meanAVERAGEReturns the average of its
arguments AVERAGEA Returns the average of its
arguments, including numbers, text, and logical
values
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CONFIDENCEReturns the confidence interval for a
population mean CORREL  Returns the correlation
coefficient between two data sets COUNTCounts
how many numbers are in the list of
arguments COUNTACounts how many values are in
the list of arguments COVARReturns covariance,
the average of the products of paired deviations
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DEVSQReturns the sum of squares of
deviations FORECASTReturns a value along a
linear trend FREQUENCYReturns a frequency
distribution as a vertical array GEOMEANReturns
the geometric mean INTERCEPTReturns the
intercept of the linear regression
line LINESTReturns the parameters of a linear
trend LOGESTReturns the parameters of an
exponential trend LOGINVReturns the inverse of
the lognormal distribution
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MEDIAN   Returns the median of the given
numbers MODE   Returns the most common value in
a data set SLOPE   Returns the slope of the
linear regression line STDEV   Estimates
standard deviation based on a sample STDEVP   Cal
culates standard deviation based on the entire
population TREND   Returns values along a linear
trend
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Analysis ToolPak

• You can use Analysis ToolPak to save steps when
  you develop complex statistical or engineering
  analyses
• You provide the data and parameters for each
  analysis the tool uses the appropriate
  statistical or engineering macro functions and
  then displays the results in an output table.
• Some tools generate charts in addition to output
  tables.

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Available tools   To view a list of available
analysis tools
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Descriptive Statistics
The Descriptive Statistics tool generates simple
descriptive statistics like mean, median, and
standard deviation for a collection of data.
In the Descriptive Statistics dialog box, specify
the cells that contain your data in the Input
Range box. Click the Summary Statistics checkbox
in the lower left corner.
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Histograms - to create a data distribution
The descriptive statistics above reported
skewness and kurtosis, which both concern the
shape of the data distribution. The Histogram
function in the Analysis ToolPak can also plot
this visually.
Generating the Bin Range for a Histogram
The Histogram tool requires that a Bin Range or
list of categories be specified. The Bin Range
represents the categories for which you want
frequency accounts.
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For example in a grading situation, the Bin Range
might include all possible test scores. Or, you
might only list ranges of scores like the table
below. Bin Range 1 counts how many people scored
1, 2, 3, etc. Bin Range 2 counts how many people
scored 0-2, 2-4, 4-6 etc.
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Creating the Histogram
After you create the Bin Range, generate the
actual histogram. In the Histogram dialog box,
the Input Range is the actual data you want to
summarize The Bin Range is the range you created
with the different categories Excel produces a
frequency distribution and a chart on another
worksheet.
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Skewness 0.4
From a histogram, you can see the skewness of the
data. The skewness measures to what degree the
data piles up on one end of the distribution. A
perfectly normal distribution like the first
example has a skewness close to 0
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Skewness 1.51
If the distribution is shaped like the second
example, it has positive skewness the
distribution approaches the axis in the positive
direction. Negative skewness means the
distribution approaches the axis in the negative
direction.