2. – residuals and exogenous shocks
18-3
Secular Trend – Example
The number of employees at Home Depot from 1993 to 2012
18-4
Cyclical Variation – Sample Chart
The annual unit sales of batteries sold by National Battery
Retails Inc. from 1991 to 2010
18-5
Seasonal Variation – Sample
Chart
Quarterly sales of Hercher Sporting G Inc, a Chicago area
sporting
goods company specializes in selling baseball and softball
equipment
to high schools, colleges and youth leagues.
4. trend.
fluctuation.
time series follows a
fairly linear trend.
18-8
Moving Average Method - Example
18-9
Example: Sears Revenue Data
0
2000
4000
6000
8000
10000
12000
14000
5. 16000
18000
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64
67 70 73
Sears Quartly Revenue 1995-2013
18-10
Linear Trend
a straight line.
18-11
Linear Trend – Using the Least
Squares Method, Regression
Analysis, and Excel
es method in Simple
Linear Regression to find the best linear
relationship between the times series and
time.
variable. That is, let t be 1 for the first year, 2
for the second, and so on.
7. 18-13
Seasonal Variation
seasons and are repeated year after year.
goods
and materials on hand to meet varying seasonal demand.
in
evaluating current sales.
18-14
Seasonally Adjusted and Detrended
Data
75604530151
15000
10000
5000
Index
75604530151
9. Detrended Data
Seas. Adj. and Detr. Data
18-15
Example: Sears Revenue Data
• The merger of Kmart and Sears closed on March 24, 2015.
• The company expected consistent quarters of decline ever
since.
• The Sears CEO Eddie Lampert’s penny-pinching ways could
have
been the major reason for the decline, according to some critics.
• “In 2010, Lampert’s capital expenditure on store
improvements
was roughly 1 percent of sales. Compare that to Macy’s, which
is 2.5 percent, and Walmart’s 8.8 percent of sales.”
• “In February, he (Lampert) flummoxed the industry by hiring
an
IBM veteran with no retail experience to run Sears and Kmart.”
• Source: “Not so fast, Eddie” by Jamens Covert, New York
post, May
22, 2015
Time Series and ForecastingTime Series and its
ComponentsSecular Trend – ExampleCyclical Variation –
Sample ChartSeasonal Variation – Sample ChartExample: Sears
Revenue DataThe Moving Average MethodMoving Average
Method - ExampleExample: Sears Revenue DataLinear
TrendLinear Trend – Using the Least Squares Method,
10. Regression Analysis, and ExcelLinear Trend PlotSeasonal
VariationSeasonally Adjusted and Detrended DataExample:
Sears Revenue Data
NotesThese data are from the Federal Reserve Bank of St. Louis
FRED2 Database. Updated 12/8/2017You have many macro
variables to choose from the general category tabs below. The
data source is the Link found in the data heading and the data
series name is in bold type above the data column for each
series.Note on the number of observationsFor the company
regression model you may need to go only as far back in history
for each X variable data series equivalent to the company
revenue history.Keep in mind that you want to use as much
information as possible but in regression the regression model
you must have each data historythe same.Logic is the Most
important factor in selecting an X variable data series.Make
sure that you can explain the correlation between the selected X
variable and the company revenue. Remember, the X variable
should be expected to be highly correlated with the company
revenue.Note on seasonalityIf your company data indicated
seasonality then you may develop a better company forecast
model with seasonal data.You may use seasonally adjusted data
for either seasonal or non seasonal company data forecast
models.
Home Price IndexFRED Graph ObservationsFederal Reserve
Economic DataLink: https://fred.stlouisfed.orgHelp:
https://fred.stlouisfed.org/help-faqEconomic Research
DivisionFederal Reserve Bank of St. LouisUSSTHPIAll-
Transactions House Price Index for the United States, Index
1980:Q1=100, Quarterly, Not Seasonally AdjustedFrequency:
Quarterlyobservation_dateUSSTHPI1975-01-0159.791975-04-
0161.101975-07-0161.261975-10-0162.431976-01-
0162.831976-04-0165.471976-07-0166.581976-10-
0167.281977-01-0169.441977-04-0172.661977-07-
0174.371977-10-0177.211978-01-0179.521978-04-
0182.721978-07-0185.211978-10-0187.471979-01-
12. 2/31/12315.083/31/13320.076/30/13325.179/30/13328.0312/31/
13330.953/31/14337.366/30/14342.309/30/14345.1712/31/1434
8.633/31/15354.936/30/15360.569/30/15363.9012/31/15367.473
/31/16374.826/30/16381.469/30/16385.0612/31/16388.903/31/1
7399.516/30/17405.46
Federal Current ExpendituresFRED Graph ObservationsFRED
Graph ObservationsFederal Reserve Economic DataFederal
Reserve Economic DataLink:
http://research.stlouisfed.org/fred2Link:
http://research.stlouisfed.org/fred2Help:
http://research.stlouisfed.org/fred2/help-faqHelp:
http://research.stlouisfed.org/fred2/help-faqEconomic Research
DivisionEconomic Research DivisionFederal Reserve Bank of
St. LouisFederal Reserve Bank of St. LouisFederal government
current expenditures, Billions of Dollars, Quarterly, Federal
Debt Held by the Public, Millions of Dollars, Quarterly,
W013RU1Q027NBEAFYGFDPUNNot Seasonally
AdjustedFrequency: QuarterlyNot Seasonally
Adjusted**DiscontinuedFrequency: Quarterly, End of
Periodobservation_dateW013RU1Q027NBEAobservation_dateF
YGFDPUN1947-01-019.9891970-01-012808141947-04-
0110.3641970-04-012749241947-07-0110.3621970-07-
012823671947-10-019.7161970-10-012912421948-01-
019.4701971-01-012920431948-04-0110.0551971-04-
012944171948-07-0110.4801971-07-013049521948-10-
0111.4521971-10-013171181949-01-0111.6541972-01-
013209871949-04-0111.6491972-04-013149761949-07-
0111.4991972-07-013195741949-10-0111.5851972-10-
013315761950-01-0113.4551973-01-013398591950-04-
0111.2631973-04-013339321950-07-0110.2101973-07-
013328381950-10-0112.0331973-10-013394321951-01-
0112.7901974-01-013424591951-04-0114.1781974-04-
013360291951-07-0115.3801974-07-013408811951-10-
0116.1071974-10-013514571952-01-0115.6051975-01-
013712011952-04-0116.6471975-04-013879051952-07-
0117.2771975-07-014113811952-10-0118.4091975-10-
24. LouisHouseholds and Nonprofit Organizations; Credit Market
Instruments; Liability, Level, Billions of Dollars,
QuarterlyHouseholds and nonprofit organizations; consumer
credit; liability, Level, Millions of Dollars, QuarterlyConsumer
Loans: Credit Cards and Other Revolving
Plans,TCMILBSHNOHNOCCIQ027SCCLACBQ158SBOG All
Commercial Banks, Percent Change at Annual Rate,
Quarterly,TDSPHousehold Debt Service Payments as a Percent
of Disposable Personal Income, HNOCCIQ027SHouseholds and
nonprofit organizations; consumer credit; liability, Level,
Millions of Dollars, Quarterly, Not Seasonally Adjusted, Not
Seasonally AdjustedPercent, Quarterly, Seasonally
AdjustedFrequency: Quarterly Level, Millions of Dollars,
Quarterly, Not Seasonally AdjustedFrequency: Quarterly, End
of PeriodFrequency: QuarterlyNot Seasonally
AdjustedFrequency: QuarterlySeasonally AdjustedFrequency:
Quarterlyobservation_dateHNOCCIQ027Sobservation_dateTCM
ILBSHNOobservation_dateHNOCCIQ027Sobservation_dateCCL
ACBQ158SBOGobservation_dateTDSP1980-04-013456371951-
10-0183.451951-10-01253509/30/002.11980-01-
0110.621971980-07-013503361952-01-0184.141952-01-
012459712/31/009.71980-04-0110.705451980-10-
013580441952-04-0188.291952-04-01268783/31/0111.01980-
07-0110.464091981-01-013539021952-07-0191.271952-07-
01279656/30/018.71980-10-0110.251131981-04-013616101952-
10-0195.671952-10-01305229/30/019.81981-01-
0110.311091981-07-013719281953-01-0197.941953-01-
013090112/31/015.11981-04-0110.456381981-10-
013778821953-04-01102.391953-04-01326723/31/020.11981-
07-0110.357841982-01-013735371953-07-01104.871953-07-
01333546/30/026.81981-10-0110.422701982-04-013808871953-
10-01108.221953-10-01346149/30/0214.51982-01-
0110.503551982-07-013868151954-01-01108.051954-01-
013274412/31/023.71982-04-0110.564081982-10-
013967181954-04-01112.381954-04-01340063/31/036.11982-
07-0110.463941983-01-013919101954-07-01115.171954-07-
42. https://research.stlouisfed.org/fred2/help-faqHelp:
https://research.stlouisfed.org/fred2/help-faqHelp:
https://research.stlouisfed.org/fred2/help-faqEconomic Research
DivisionEconomic Research DivisionEconomic Research
DivisionEconomic Research DivisionFederal Reserve Bank of
St. LouisFederal Reserve Bank of St. LouisFederal Reserve
Bank of St. LouisFederal Reserve Bank of St. LouisE-
Commerce Retail Sales as a Percent of Total Sales, Percent,
Quarterly,E-Commerce Retail Sales as a Percent of Total Sales,
Percent, QuarterlyE-Commerce Retail Sales, Millions of
Dollars, QuarterlyE-Commerce Retail Sales, Millions of
Dollars, Quarterly, ECOMPCTSAECOMPCTNSAECOMSA
Seasonally AdjustedECOMNSAFrequency: QuarterlySeasonally
AdjustedFrequency: Quarterly Not Seasonally
AdjustedFrequency: QuarterlyFrequency: QuarterlyNot
Seasonally
Adjustedobservation_dateECOMPCTSAobservation_dateECOM
PCTNSAobservation_dateECOMSAobservation_dateECOMNSA
9/30/990.69/30/990.79/30/9944489/30/99526612/31/990.812/31/
990.812/31/99581612/31/9955633/31/000.93/31/000.83/31/0065
013/31/0060716/30/001.06/30/000.96/30/0073336/30/0069029/3
0/001.09/30/001.19/30/0077669/30/00908012/31/001.112/31/00
1.112/31/00822012/31/0078893/31/011.13/31/011.03/31/018357
3/31/0178226/30/011.16/30/011.06/30/0182766/30/0177599/30/
011.29/30/011.39/30/0193079/30/011080812/31/011.312/31/011
.312/31/011000012/31/0196303/31/021.43/31/021.33/31/021075
63/31/02100806/30/021.56/30/021.46/30/02114786/30/0210766
9/30/021.59/30/021.79/30/02122279/30/021417712/31/021.612/
31/021.712/31/021279612/31/02123693/31/031.73/31/031.63/31
/03137793/31/03129906/30/031.86/30/031.76/30/03147876/30/0
3139269/30/031.99/30/032.09/30/03155859/30/031792712/31/0
32.012/31/032.012/31/031671912/31/03162103/31/042.03/31/04
1.93/31/04175103/31/04165136/30/042.16/30/042.06/30/041849
46/30/04174039/30/042.29/30/042.49/30/04196449/30/0422563
12/31/042.312/31/042.412/31/042081612/31/04201793/31/052.4
3/31/052.33/31/05222313/31/05209856/30/052.56/30/052.46/30/
44. Population & EarningFRED Graph ObservationsFRED Graph
ObservationsFederal Reserve Economic DataFederal Reserve
Economic DataLink: https://research.stlouisfed.org/fred2Link:
https://research.stlouisfed.org/fred2Help:
https://research.stlouisfed.org/fred2/help-faqHelp:
https://research.stlouisfed.org/fred2/help-faqEconomic Research
DivisionEconomic Research DivisionFederal Reserve Bank of
St. LouisFederal Reserve Bank of St. LouisWorking Age
Population 15 to 64Employed full time: Median usual weekly
nominal earnings (second quartile): Wage and salary workers:
16 years and over, Dollars, Quarterly,
LFWA64TTUSQ647NLES1252881500QAverage Weekly
DollarsFrequency: QuarterlyNot Seasoonally
AdjustedFrequency: QuarterlySeasonally
Adjustedobservation_dateLFWA64TTUSQ647Nobservation_dat
eLES1252881500Q1955-01-01955523331979-01-012321955-04-
01958630001979-04-012391955-07-01961050001979-07-
012431955-10-01962970001979-10-012481956-01-
01965046671980-01-012541956-04-01967193331980-04-
012571956-07-01970386671980-07-012661956-10-
01972473331980-10-012691957-01-01974553331981-01-
012761957-04-01976966671981-04-012791957-07-
01980333331981-07-012851957-10-01983730001981-10-
012921958-01-01986880001982-01-012951958-04-
01989260001982-04-013011958-07-01991600001982-07-
013031958-10-01994923331982-10-013061959-01-
01998483331983-01-013091959-04-011002023331983-04-
013111959-07-011005273331983-07-013161959-10-
011008006671983-10-013161960-01-011014806671984-01-
013211960-04-011017583331984-04-013231960-07-
011020436671984-07-013271960-10-011023503331984-10-
013331961-01-011027060001985-01-013341961-04-
011030023331985-04-013471961-07-011032706671985-07-
013451961-10-011033580001985-10-013481962-01-
011034730001986-01-013521962-04-011031246671986-04-
013581962-07-011036033331986-07-013591962-10-
53. Economic DataLink: http://research.stlouisfed.org/fred2Help:
http://research.stlouisfed.org/fred2/help-faqEconomic Research
DivisionFederal Reserve Bank of St. LouisGDPPOTReal
Potential Gross Domestic Product, Billions of Chained 2009
Dollars, Quarterly, Not Seasonally AdjustedNote that this is not
real GDP but GDP adjusted to full employmentFrequency:
Quarterlyobservation_dateGDPPOT1949-01-012011.11949-04-
012038.01949-07-012065.21949-10-012092.61950-01-
012120.11950-04-012147.31950-07-012174.71950-10-
012202.61951-01-012231.01951-04-012260.91951-07-
012291.61951-10-012323.01952-01-012355.51952-04-
012389.31952-07-012422.61952-10-012454.81953-01-
012484.41953-04-012510.51953-07-012534.31953-10-
012556.01954-01-012574.61954-04-012591.41954-07-
012607.11954-10-012622.41955-01-012638.81955-04-
012655.11955-07-012671.61955-10-012688.41956-01-
012705.71956-04-012723.21956-07-012741.41956-10-
012760.51957-01-012780.91957-04-012803.11957-07-
012826.51957-10-012850.91958-01-012876.51958-04-
012902.31958-07-012928.61958-10-012955.41959-01-
012981.81959-04-013009.01959-07-013036.91959-10-
013065.41960-01-013095.11960-04-013125.71960-07-
013156.81960-10-013188.31961-01-013219.81961-04-
013250.71961-07-013281.91961-10-013313.81962-01-
013346.41962-04-013380.81962-07-013416.41962-10-
013453.01963-01-013491.41963-04-013530.21963-07-
013569.61963-10-013609.31964-01-013648.41964-04-
013687.91964-07-013727.81964-10-013768.21965-01-
013809.31965-04-013850.31965-07-013891.91965-10-
013934.31966-01-013977.31966-04-014022.01966-07-
014067.71966-10-014114.51967-01-014162.81967-04-
014211.81967-07-014261.31967-10-014311.11968-01-
014360.51968-04-014411.01968-07-014461.31968-10-
014510.91969-01-014559.51969-04-014606.21969-07-
014651.21969-10-014694.31970-01-014734.21970-04-
014771.51970-07-014807.51970-10-014842.61971-01-