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TIME SERIES FORECASTING
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DECOMPOSITION OF TIME
SERIES
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Visualizing Seasonality
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Visualization of Seasonality
Helps to see the nature of seasonality
But does not help in quantification
4
12-Jan-18
Objective of this lesson is to extract time series
components numerically to evaluate their
importance in the historical pattern of the data
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This study aimed to compare teacher feedback, student self-regulated learning, and the relationship between these factors in high-achieving versus low-achieving secondary schools. Specifically, the study sought to determine if there were differences in (1) the types of mathematics teacher feedback, (2) students' self-regulated learning in mathematics, and (3) the relationships between teacher feedback and student self-regulated learning between high- and low-achieving schools. The study was motivated by research suggesting school climate and culture can impact these factors differently in high versus low performing schools.

correlation between online
Why Decompose
• To understand revenue generation without the quarterly
effects
̶ De-seasonalize the series
̶ Estimate and adjust by seasonality
• Compare the long-term movement of the series (Trend) vis-a-
vis short-term movement (seasonality) to understand which
has the higher influence
• If revenue for multiple sector are to be compared and if the
sectors show non-uniform seasonality, de-seasonalized series
needs to be compared
5
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What is Seasonality?
Seasonality is the relative increase or decrease of sales
(demand or consumption) every period(quarter or
month or week) compared to the yearly average
6
Heuristic example with 4 quarters
Yearly sale = 400 units
Quarterly average = 100 units
Actual sales
Q1 = 80 units Q2 = 70 units Q3 = 200 units
Q4 = 50 units
Seasonality estimate
Q1 = -20 Q2= -30 Q3 = +100 Q4 = - 50
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Decomposition Model
7
Yt : time series value (actual data) at period t.
St : seasonal component (index) at period t.
Tt : trend cycle component at period t.
It : irregular (remainder) component at period t
Additive model: Observation = Trend + Seasonality + Error
Yt = Tt + St + It
Useful when the seasonal variation is relatively constant over time
Multiplicative model: Observation = Trend * Seasonality * Error
Yt = Tt * St * It
Multiplicative models are more realistic
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Caselet I: Quarterly Revenue
• Quarterly revenue is a sum of Trend, Seasonality and
Irregular component
• Would like to understand relative effects of the 4 quarters
• Would like to understand the long-term movement of the
series, after seasonal effect has been eliminated
• Example of an Additive Seasonality Model
Yt = Tt + St + It
Revenue = Trend + Seasonality + Error
8
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Correlational research establishes relationships between variables without determining cause, using dependent variables only. It demonstrates relationships exist but not causation. A correlation coefficient measures the direction and strength of relationships between two variables on a scale from -1 to 1, with higher positive or negative values indicating stronger linear relationships. Statistical analysis evaluates numerical data through correlation coefficients and scatter plots to describe variable relationships.

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Correlational research establishes relationships between variables but does not determine cause-and-effect. It uses correlation coefficients to measure the direction and strength of relationships between two variables. Statistical analysis of scores from each individual on two variables can show their relationship graphically in a scatter plot. Experimental research determines cause-and-effect relationships, while descriptive research explores characteristics without determining relationships.

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PE ratio is a metric that compares a company's stock price to its earnings per share. It indicates how much an investor pays for each dollar of earnings. A PE ratio is calculated by dividing the current stock price by the earnings per share. PE ratios help investors compare similar companies and determine if a stock is undervalued, appropriately priced, or overvalued. Factors like growth rates, profit margins, returns, macroeconomic conditions, and intangible assets can impact a company's PE ratio. Comparing a company's PE ratio to its industry peers provides useful insight into how the market values that company.

Decomposition in R
IncDec<-stl(Income, s.window='p') constant seasonality
plot(IncDec)
IncDec
IncDec7<-stl(Income, s.window=7) seasonality changes
plot(IncDec7)
IncDec
DeseasonRevenue <- (IncDec7$time.series[,2]+IncDec7$time.series[,3])
ts.plot(DeseasonRevenue, Revenue, col=c("red", "blue"), main="Comparison
of Revenue and Deseasonalized Revenue")
9
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Caselet I: Quarterly Revenue
10
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Caselet I: Quarterly Revenue
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Deseasonalized
Revenue Seasonal
fluctuation
comparatively
insignificant
than YOY
movement
Caselet I: Quarterly Revenue
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This thesis examines whether implied volatility from options prices can provide additional information for forecasting realized volatility compared to historical volatility models. The study analyzes the S&P 500 index and VIX in the US, and the Euro Stoxx 50 index and VSTOXX in Europe from 2005 to 2019. GARCH and EGARCH models are estimated with and without implied volatility to evaluate its information content. Out-of-sample forecasts are generated and evaluated using statistical tests. The results suggest that including implied volatility improves model fit but does not necessarily lead to more accurate volatility forecasts compared to historical volatility alone.

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1. An entrepreneur organizes and operates a new business venture, taking on risks to produce goods or services. A business plan documents business objectives, operations, finance, and ownership to help obtain loans and guide the business. 2. Businesses want to grow internally through new branches or externally through mergers and acquisitions to benefit from economies of scale, increased market share, and access to new markets. However, growth brings challenges like difficulty controlling larger operations. 3. Not all businesses grow - some stay small due to factors like their industry, market size, or owners' objectives. New businesses are also at high risk of failure due to lack of experience, understanding of the market, sales, and financial resources compared

Caselet II: Champagne Sales
• Monthly sales is a sum of Trend, Seasonality and Irregular
component
• Would like to understand relative effects of the 12 months
• Would like to understand whether there is at all any
movement of the sales series after the seasonal fluctuations
are eliminated
• Example of an Additive Seasonality Model
Yt = Tt + St + It
Sales = Trend + Seasonality + Error
13
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Caselet II: Champagne Sales
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Caselet II: Champagne Sales
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Caselet II: Champagne Sales
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Caselet II: Champagne Sales
• Practically there is no effect of any YOY movement
• The changes we see are almost all due to monthly
fluctuations
17
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Caselet II: Champagne Sales
Critical look at seasonality
• During first part of the
year almost no change
• Sharp drop in sales in
August
• Last 4 months show
steep increase in sales
18
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Caselet III: Passenger Volume
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Caselet III: Passenger Volume
• There is a definite upward movement YOY
• Seasonal fluctuations increasing as total volume increases
• Example of an Multiplicative Seasonality Model
Yt = Tt * St * It
Volume= Trend *Seasonality * Error
20
• Need logarithmic transformation to convert into an additive
series
Log(Vol) = log(Trend) + log(Seasonality) + log(Error)
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原版制作【微信:A575476】【(NC毕业证)尼亚加拉学院毕业证成绩单offer】【微信:A575476】(留信学历认证永久存档查询)采用学校原版纸张(包括:隐形水印,阴影底纹,钢印LOGO烫金烫银,LOGO烫金烫银复合重叠,文字图案浮雕,激光镭射,紫外荧光,温感,复印防伪)行业标杆!精益求精,诚心合作,真诚制作!多年品质 ,按需精细制作,24小时接单,全套进口原装设备,十五年致力于帮助留学生解决难题,业务范围有加拿大、英国、澳洲、韩国、美国、新加坡,新西兰等学历材料,包您满意。 【业务选择办理准则】 一、工作未确定,回国需先给父母、亲戚朋友看下文凭的情况,办理一份就读学校的毕业证【微信:A575476】文凭即可 二、回国进私企、外企、自己做生意的情况,这些单位是不查询毕业证真伪的,而且国内没有渠道去查询国外文凭的真假,也不需要提供真实教育部认证。鉴于此,办理一份毕业证【微信:A575476】即可 三、进国企,银行,事业单位,考公务员等等,这些单位是必需要提供真实教育部认证的,办理教育部认证所需资料众多且烦琐,所有材料您都必须提供原件,我们凭借丰富的经验,快捷的绿色通道帮您快速整合材料,让您少走弯路。 留信网认证的作用: 1:该专业认证可证明留学生真实身份【微信:A575476】 2:同时对留学生所学专业登记给予评定 3:国家专业人才认证中心颁发入库证书 4:这个认证书并且可以归档倒地方 5:凡事获得留信网入网的信息将会逐步更新到个人身份内,将在公安局网内查询个人身份证信息后,同步读取人才网入库信息 6:个人职称评审加20分 7:个人信誉贷款加10分 8:在国家人才网主办的国家网络招聘大会中纳入资料,供国家高端企业选择人才 → 【关于价格问题(保证一手价格) 我们所定的价格是非常合理的,而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格,因为我想坦诚对待大家 不想跟大家在价格方面浪费时间 对于老客户或者被老客户介绍过来的朋友,我们都会适当给一些优惠。 选择实体注册公司办理,更放心,更安全!我们的承诺:可来公司面谈,可签订合同,会陪同客户一起到教育部认证窗口递交认证材料,客户在教育部官方认证查询网站查询到认证通过结果后付款,不成功不收费! 办理(NC毕业证)尼亚加拉学院毕业证【微信:A575476】外观非常精致,由特殊纸质材料制成,上面印有校徽、校名、毕业生姓名、专业等信息。 办理(NC毕业证)尼亚加拉学院毕业证【微信:A575476】格式相对统一,各专业都有相应的模板。通常包括以下部分: 校徽:象征着学校的荣誉和传承。 校名:学校英文全称 授予学位:本部分将注明获得的具体学位名称。 毕业生姓名:这是最重要的信息之一,标志着该证书是由特定人员获得的。 颁发日期:这是毕业正式生效的时间,也代表着毕业生学业的结束。 其他信息:根据不同的专业和学位,可能会有一些特定的信息或章节。 办理(NC毕业证)尼亚加拉学院毕业证【微信:A575476】价值很高,需要妥善保管。一般来说,应放置在安全、干燥、防潮的地方,避免长时间暴露在阳光下。如需使用,最好使用复印件而不是原件,以免丢失。 综上所述,办理(NC毕业证)尼亚加拉学院毕业证【微信:A575476 】是证明身份和学历的高价值文件。外观简单庄重,格式统一,包括重要的个人信息和发布日期。对持有人来说,妥善保管是非常重要的。

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Caselet III: Passenger Volume
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Caselet III: Passenger Volume
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Caselet III: Passenger Volume
Write conclusions on your own:
• Which part contributes more – Trend or Seasonality?
• Which month(s) show high passenger volume compared to
yearly average?
• Which month(s) show low passenger volume compared to
yearly average?
23
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Caselet III: Passenger Volume
Critical look at seasonality
• From Feb passenger
volume starts
increasing
• Jun – Sep shows high
volume
• Jul – Aug has highest
vol
• Dec shows slight
increase
24
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mumbai rainfalls
Lajpat Nagar @ℂall @Girls ꧁❤ 9873777170 ❤꧂VIP Ginni Singh Top Model Safe
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Next Step
Ultimate goal of understanding the time series
components is to forecast for the coming years
In the next lesson we apply forecast by
decomposition, as well as learn about other
forecast methods
25
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TS Decomposition IN data Time Series Fore

  • 1. TIME SERIES FORECASTING 12-Jan-18 1 haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 2. DECOMPOSITION OF TIME SERIES 12-Jan-18 2 haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 3. Visualizing Seasonality 12-Jan-18 3 haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 4. Visualization of Seasonality Helps to see the nature of seasonality But does not help in quantification 4 12-Jan-18 Objective of this lesson is to extract time series components numerically to evaluate their importance in the historical pattern of the data haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 5. Why Decompose • To understand revenue generation without the quarterly effects ̶ De-seasonalize the series ̶ Estimate and adjust by seasonality • Compare the long-term movement of the series (Trend) vis-a- vis short-term movement (seasonality) to understand which has the higher influence • If revenue for multiple sector are to be compared and if the sectors show non-uniform seasonality, de-seasonalized series needs to be compared 5 12-Jan-18 haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 6. What is Seasonality? Seasonality is the relative increase or decrease of sales (demand or consumption) every period(quarter or month or week) compared to the yearly average 6 Heuristic example with 4 quarters Yearly sale = 400 units Quarterly average = 100 units Actual sales Q1 = 80 units Q2 = 70 units Q3 = 200 units Q4 = 50 units Seasonality estimate Q1 = -20 Q2= -30 Q3 = +100 Q4 = - 50 haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 7. Decomposition Model 7 Yt : time series value (actual data) at period t. St : seasonal component (index) at period t. Tt : trend cycle component at period t. It : irregular (remainder) component at period t Additive model: Observation = Trend + Seasonality + Error Yt = Tt + St + It Useful when the seasonal variation is relatively constant over time Multiplicative model: Observation = Trend * Seasonality * Error Yt = Tt * St * It Multiplicative models are more realistic haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 8. Caselet I: Quarterly Revenue • Quarterly revenue is a sum of Trend, Seasonality and Irregular component • Would like to understand relative effects of the 4 quarters • Would like to understand the long-term movement of the series, after seasonal effect has been eliminated • Example of an Additive Seasonality Model Yt = Tt + St + It Revenue = Trend + Seasonality + Error 8 haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 9. Decomposition in R IncDec<-stl(Income, s.window='p') constant seasonality plot(IncDec) IncDec IncDec7<-stl(Income, s.window=7) seasonality changes plot(IncDec7) IncDec DeseasonRevenue <- (IncDec7$time.series[,2]+IncDec7$time.series[,3]) ts.plot(DeseasonRevenue, Revenue, col=c("red", "blue"), main="Comparison of Revenue and Deseasonalized Revenue") 9 haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 10. Caselet I: Quarterly Revenue 10 haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 11. 12-Jan-18 11 Caselet I: Quarterly Revenue haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 12. 12-Jan-18 12 Deseasonalized Revenue Seasonal fluctuation comparatively insignificant than YOY movement Caselet I: Quarterly Revenue haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 13. Caselet II: Champagne Sales • Monthly sales is a sum of Trend, Seasonality and Irregular component • Would like to understand relative effects of the 12 months • Would like to understand whether there is at all any movement of the sales series after the seasonal fluctuations are eliminated • Example of an Additive Seasonality Model Yt = Tt + St + It Sales = Trend + Seasonality + Error 13 haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 14. Caselet II: Champagne Sales 12-Jan-18 14 haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 15. Caselet II: Champagne Sales 12-Jan-18 15 haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 16. Caselet II: Champagne Sales 12-Jan-18 16 haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 17. Caselet II: Champagne Sales • Practically there is no effect of any YOY movement • The changes we see are almost all due to monthly fluctuations 17 haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 18. Caselet II: Champagne Sales Critical look at seasonality • During first part of the year almost no change • Sharp drop in sales in August • Last 4 months show steep increase in sales 18 haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 19. Caselet III: Passenger Volume 12-Jan-18 19 haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 20. Caselet III: Passenger Volume • There is a definite upward movement YOY • Seasonal fluctuations increasing as total volume increases • Example of an Multiplicative Seasonality Model Yt = Tt * St * It Volume= Trend *Seasonality * Error 20 • Need logarithmic transformation to convert into an additive series Log(Vol) = log(Trend) + log(Seasonality) + log(Error) haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 21. Caselet III: Passenger Volume 12-Jan-18 21 haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 22. Caselet III: Passenger Volume 12-Jan-18 22 haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 23. Caselet III: Passenger Volume Write conclusions on your own: • Which part contributes more – Trend or Seasonality? • Which month(s) show high passenger volume compared to yearly average? • Which month(s) show low passenger volume compared to yearly average? 23 haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 24. Caselet III: Passenger Volume Critical look at seasonality • From Feb passenger volume starts increasing • Jun – Sep shows high volume • Jul – Aug has highest vol • Dec shows slight increase 24 haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.
  • 25. Next Step Ultimate goal of understanding the time series components is to forecast for the coming years In the next lesson we apply forecast by decomposition, as well as learn about other forecast methods 25 12-Jan-18 Thank you haritika74@gmail.com BABIINTLMAY19001 This file is meant for personal use by haritika74@gmail.com only. Sharing or publishing the contents in part or full is liable for legal action.