Trend and seasonal components can be extracted from time series data. The trend component shows a long-term increase or decrease in the data. The seasonal component shows regular fluctuations that occur with a fixed periodicity, such as monthly or yearly. Decomposition methods like moving averages can be used to separate trend, seasonal, and irregular components. The seasonal factors are then used to forecast future values by scaling the trend projection.
Moving avg & method of least squareHassan Jalil
A quantitative method of forecasting or smoothing a time series by averaging each successive group (no. of observations) of data values.
Term MOVING is used because it is obtained by summing and averaging the values from a given no of periods, each time deleting the oldest value and adding a new value.
The moving average formula of demand forecasting is explained herein with the help of an example in an easily understandable way. The ppt contains the meaning and formula of moving average along with an example.
Moving avg & method of least squareHassan Jalil
A quantitative method of forecasting or smoothing a time series by averaging each successive group (no. of observations) of data values.
Term MOVING is used because it is obtained by summing and averaging the values from a given no of periods, each time deleting the oldest value and adding a new value.
The moving average formula of demand forecasting is explained herein with the help of an example in an easily understandable way. The ppt contains the meaning and formula of moving average along with an example.
A method that uses measurable, historical data observations, to make forecasts by calculating the weighted average of the current period’s actual value and forecast, with a trend adjustment added in
Time Series Analysis - 1 | Time Series in R | Time Series Forecasting | Data ...Simplilearn
This Time Series Analysis (Part-1) in R presentation will help you understand what is time series, why time series, components of time series, when not to use time series, why does a time series have to be stationary, how to make a time series stationary and at the end, you will also see a use case where we will forecast car sales for 5th year using the given data. A time series is a sequence of data being recorded at specific time intervals. The past values are analyzed to forecast a future which is time-dependent. Compared to other forecast algorithms, with time series we deal with a single variable which is dependent on time. So, lets deep dive into this presentation and understand what is time series and how to implement time series using R.
Below topics are explained in this "Time Series in R Tutorial" -
1. Why time series?
2. What is time series?
3. Components of a time series
4. When not to use time series?
5. Why does a time series have to be stationary?
6. How to make a time series stationary?
7. Example: Forcast car sales for the 5th year
Become an expert in data analytics using the R programming language in this data science certification training course. You’ll master data exploration, data visualization, predictive analytics and descriptive analytics techniques with the R language. With this data science course, you’ll get hands-on practice on R CloudLab by implementing various real-life, industry-based projects in the domains of healthcare, retail, insurance, finance, airlines, music industry, and unemployment.
Why learn Data Science with R?
1. This course forms an ideal package for aspiring data analysts aspiring to build a successful career in analytics/data science. By the end of this training, participants will acquire a 360-degree overview of business analytics and R by mastering concepts like data exploration, data visualization, predictive analytics, etc
2. According to marketsandmarkets.com, the advanced analytics market will be worth $29.53 Billion by 2019
3. Wired.com points to a report by Glassdoor that the average salary of a data scientist is $118,709
4. Randstad reports that pay hikes in the analytics industry are 50% higher than IT
The Data Science with R is recommended for:
1. IT professionals looking for a career switch into data science and analytics
2. Software developers looking for a career switch into data science and analytics
3. Professionals working in data and business analytics
4. Graduates looking to build a career in analytics and data science
5. Anyone with a genuine interest in the data science field
6. Experienced professionals who would like to harness data science in their fields
Learn more at: https://www.simplilearn.com/
A method that uses measurable, historical data observations, to make forecasts by calculating the weighted average of the current period’s actual value and forecast, with a trend adjustment added in
Time Series Analysis - 1 | Time Series in R | Time Series Forecasting | Data ...Simplilearn
This Time Series Analysis (Part-1) in R presentation will help you understand what is time series, why time series, components of time series, when not to use time series, why does a time series have to be stationary, how to make a time series stationary and at the end, you will also see a use case where we will forecast car sales for 5th year using the given data. A time series is a sequence of data being recorded at specific time intervals. The past values are analyzed to forecast a future which is time-dependent. Compared to other forecast algorithms, with time series we deal with a single variable which is dependent on time. So, lets deep dive into this presentation and understand what is time series and how to implement time series using R.
Below topics are explained in this "Time Series in R Tutorial" -
1. Why time series?
2. What is time series?
3. Components of a time series
4. When not to use time series?
5. Why does a time series have to be stationary?
6. How to make a time series stationary?
7. Example: Forcast car sales for the 5th year
Become an expert in data analytics using the R programming language in this data science certification training course. You’ll master data exploration, data visualization, predictive analytics and descriptive analytics techniques with the R language. With this data science course, you’ll get hands-on practice on R CloudLab by implementing various real-life, industry-based projects in the domains of healthcare, retail, insurance, finance, airlines, music industry, and unemployment.
Why learn Data Science with R?
1. This course forms an ideal package for aspiring data analysts aspiring to build a successful career in analytics/data science. By the end of this training, participants will acquire a 360-degree overview of business analytics and R by mastering concepts like data exploration, data visualization, predictive analytics, etc
2. According to marketsandmarkets.com, the advanced analytics market will be worth $29.53 Billion by 2019
3. Wired.com points to a report by Glassdoor that the average salary of a data scientist is $118,709
4. Randstad reports that pay hikes in the analytics industry are 50% higher than IT
The Data Science with R is recommended for:
1. IT professionals looking for a career switch into data science and analytics
2. Software developers looking for a career switch into data science and analytics
3. Professionals working in data and business analytics
4. Graduates looking to build a career in analytics and data science
5. Anyone with a genuine interest in the data science field
6. Experienced professionals who would like to harness data science in their fields
Learn more at: https://www.simplilearn.com/
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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3. Trend Component
• a long-term increase or decrease in the datawhich
might not be linear. Sometimes the trend might
changedirection as time increases
Back
4. Seasonal Component
• exists when a series exhibits regularfluctuations based
on the season (e.g. every month/quarter/year).
Seasonality is always of a fixed and known period.
6. Trend Projection
• We can calculate trend projection with the method of least squares, the formula for the trend projection is shown below :
• Tt = b0 + b1t
• Where the symbol mean :
• Tt : Trend forecast for the time period t
• b1 : slope of the trend line
• b0 : trend line projection for the time 0
• And we also have to find b0 too, and the formula is down below :
• Where the symbol mean :
• Yt = observed value of the time series at time period t
• = average time period for the n observations
• = average of the observed values for Yt
7. • but we have to find the b1 first, and we can find
with the formula below:
8. • And we also have to find b0 too, and the formula is down
below :
Yt = observed value of the time series at time period t
= average time period for the n observations
= average of the observed values for Yt
9. Example
• The number of MONSTA X show appeared in korean
music bank in each of the last 12 month is listed on the
table below. Forecast the number of monsta x show’s will
perform in the next year on the first month (January) using
the least square methodThe number of MONSTA X show
appeared in korean music bank in each of the last 12
month is listed on the table below. Forecast the number of
monsta x show’s will perform in the next year on the first
month (January) using the least square method
10. MONTH MX SHOWS
January 23
February 30
March 29
April 40
May 55
June 42
July 65
August 78
September 73
October 68
November 70
December 80
11. MONTH t Yt tYt t2
January 1 23 23 1
February 2 30 60 4
March 3 29 87 9
April 4 40 160 16
May 5 55 275 25
June 6 42 252 36
July 7 65 455 49
August 8 78 624 64
September 9 73 657 81
October 10 68 680 100
November 11 70 770 121
December 12 80 960 144
SUM 78 653 5003 650
12. • = 78 / 12 = 6.5
• = 653 / 12 = 54.4166667 using round up formula in excel
54.42
• b1 = (12)(5003)-(78)(653)/(12)(650)-(78)^ = 5.3041958
• using round up formula in excel 5.31
• b0 = - b1 = 54.42 – 5.31(6.5) = 19.905 with roundup to 19.91
• T13 = 19.91 + (5.31)(13) = 88.94
Y
Y
13. Monsta x appear in music bank
• forecast for January (month 13) using a three-period
(n=3) weighted moving average with weight of .5, .3, .2
for the newest to oldest data, respectively. Then,
compare this month 13 weighted moving average
forecast with the month 13 trend projection forecast.
14. Three-month weighted moving average
• The forecast for January will be the weighted average of
the preceding three months: October, November,
December
• F13 = .2 Y oct + .3Y nov + .5Y dec
• = .2(68)+.3(70)+.5(80) = 74.6
16. Note : The meaning of the symbols
• Tt : Trend forecast for the time period t
• b1 : slope of the trend line
• b0 : trend line projection for the time 0
17. Trend and Seasonal
• A table below will explain Evelyn’s Bakery Shop weekly
sales during four different seasons; 1.) Mother’s Day 2.)
Christmas Day, 3.) New Year, and 4.) Valentine’s DaySeason
Year Mother’s Day Christmas Day New Year Valentine
’s Day
2015 1999 3867 5346 3097
2016 2005 2345 7777 1089
2017 1857 8907 8234 2011
2018 1230 6754 1089 6435
18. First Step : Calculate CMA (Centered Moving Average)
There are three distinct seasons in each year.
Hence, take a three-season moving average to
eliminate seasonal and irregular factors.
• 1st CMA: 1999+3867+5346+3097/4 = 3577,25
• 2nd CMA: 3867+5346+3097+2005/4 =
3578,75
• 3rd CMA: 5346+3097+2005+2345/4 = 3198,25
• 4th CMA: 3097+2005+2345+7777/4= 3806
• Etc.
19. Second Step: Center the CMAs on integer-valued periods
• The first centered moving average computed in step 1 (11986,25) will be centered on
season 2 of year 1. Note that the moving averages from step 1 center themselves on
integer-valued periods because n is an odd number.
Year Season Dollar Sales (Yt) Moving Average
2015 1 1999
2 3867 3577,25
3 5346 3578,75
4 3097 3198,25
2016 1 2005 3806
2 2345 3304
3 7777 3267
4 1089 4907,5
2017 1 1857 5021,75
2 8907 5252,25
3 8234 5095,5
4 2011 4557,25
2018 1 1230 2771
2 6754 3881,5
3 1089
4 6435
20. Third Step: Determine the seasonal and irregular factors
(St It )
Isolate the trend and cyclical components. For each period t, this is given by:
St It = Yt /(Moving Average for period t )
Year Season Dollar Sales (Yt) Moving Average StIt
2015 1 1999
2 3867 3577,25 1,08 (3867/3577,25)
3 5346 3578,75 1,49
4 3097 3198,25 0,96
2016 1 2005 3806 0,52
2 2345 3304 0,7
3 7777 3267 2,38
4 1089 4907,5 0,22
2017 1 1857 5021,75 0,36
2 8907 5252,25 1,69
3 8234 5095,5 1,61
4 2011 4557,25 0,44
2018 1 1230 2771 0,44
2 6754 3881,5 1,74
3 1089
4 6435
21. Fourth Step: Determine the average seasonal factors
Averaging all St It values corresponding to that
season:
Season 1: 0,52+0,36+0,44/3 = 0,44
Season 2: 1,08 + 0,70+0,36+1,74/4=2,57
Season 3: 1,49+2,38+1,61/3= 1,82
Season 4: 0,96+0,22+0,44/3= 1,32
0,44+2,57+1,82+1,32= 6,15
22. Fifth Step: Scale the seasonal factors (St )
Year Season Dollar Sales (Yt) Moving Average StIt ScaledSt
2015 1 1999 0,28
2 3867 3577,25 1,08 (3867/3577,25) 1,67
3 5346 3578,75 1,49 1,18
4 3097 3198,25 0,96 0,86
2016 1 2005 3806 0,52 0,28
2 2345 3304 0,7 1,67
3 7777 3267 2,38 1,18
4 1089 4907,5 0,22 0,86
2017 1 1857 5021,75 0,36 0,28
2 8907 5252,25 1,69 1,67
3 8234 5095,5 1,61 1,18
4 2011 4557,25 0,44 0,86
2018 1 1230 2771 0,44 0,28
2 6754 3881,5 1,74 1,67
3 1089 1,18
4 6435 0,86
Average the seasonal factors = (0,44+2,57+1,82+1,32)/4 = 1,53. Then, divide each seasonal factor by the average of
the seasonal factors.
Season 1: 0,44/1,53= 0,28
Season 2: 2,57/1,53= 1,67
Season 3: 1,82/1,53= 1,18
Season 4: 1,32/1,53= 0,86
0,28+1,67+1,18+0,86= 3,99
23. Seventh Step: Determine a trend line of the deseasonalized
data
• Using the least squares method for t = 1, 2, ..., 16, gives:
• Tt = 1580.11 + 33.96t
24. Eight Step: Determine the deseasonalized predictions
• Substitute t = 17, 18, 19, and 20 into the least squares
equation:
• T17 = 1580.11 + (33.96)(17) = 2157,43
• T18 = 1580.11 + (33.96)(18) = 2191,39
• T19 = 1580.11 + (33.96)(19) = 2225,35
• T20 = 1580.11 + (33.96)(20) = 2259,31
25. Ninth Step: Take into account the seasonality
• Multiply each deseasonalized prediction by its seasonal
factor to give the following forecasts for year 5
• Season 1: (0,28)(2157,43) = 604,08
• Season 2: (1.67)(2191,39) = 3659,62
• Season 3: ( 1,18)(2225,35) = 2625,91
• Season 4: (0,86)(2259,31) = 1943
