Smoothing techniques - Revision history

Bosmana fem: /* Describing seasonal variations */

2023-04-10T21:57:41Z

Describing seasonal variations

← Older revision		Revision as of 21:57, 10 April 2023
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	Using the median value over the window rather than the mean generates a moving median that is more robust to outliers than the mean. In such case, the Excel © formula should be =MEDIAN(B2:B6) in cell C4 and copied over the range. Note that functions in MS-Excel© may vary according to language.		Using the median value over the window rather than the mean generates a moving median that is more robust to outliers than the mean. In such case, the Excel © formula should be =MEDIAN(B2:B6) in cell C4 and copied over the range. Note that functions in MS-Excel© may vary according to language.

	===FEM Editor 2007~~===~~		<div style="display: inline-block; width: 25%; vertical-align: top; border: 1px solid #000; background-color: #d7effc; padding: 10px; margin: 5px;">
	* Denis Coulombier		'''FEM PAGE CONTRIBUTORS 2007'''
	~~===~~Original FEM Authors~~===~~		;FEM Editor 2007
	* Christophe Paquet		:Denis Coulombier
	* Arnold Tarantola		;Original FEM Authors
	* Philippe Quenel		:Christophe Paquet
	* Nada Ghosn		:Arnold Tarantola
	~~===~~FEM Contributors~~===~~		:Philippe Quenel
	* Denis Coulombier		:Nada Ghosn
	* Lisa Lazareck		;FEM Contributors
	* Vladimir Prikazsky		:Denis Coulombier
			:Lisa Lazareck
			:Vladimir Prikazsky
			</div>

	[[Category:Analysis by time characteristics]]		[[Category:Analysis by time characteristics]]

Bosmana fem at 20:23, 22 March 2023

2023-03-22T20:23:19Z

← Older revision		Revision as of 20:23, 22 March 2023
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	* Lisa Lazareck		* Lisa Lazareck
	* Vladimir Prikazsky		* Vladimir Prikazsky


			[[Category:Analysis by time characteristics]]

Bosmana fem: /* Describing seasonal variations */

2022-12-18T14:48:01Z

Describing seasonal variations

← Older revision		Revision as of 14:48, 18 December 2022
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	Figure 3: Crude data, and 15 weeks moving average		Figure 3: Crude data, and 15 weeks moving average

	[[File:~~Seasonality~~.png\|600px\|frame\|none]]		[[File:seasonality.png\|600px\|frame\|none]]

	Principles for calculating moving averages		Principles for calculating moving averages
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	\|}		\|}

	Using the median value over the window rather than the mean generates a moving median ~~which~~ is more robust to outliers than the mean. In such case, the Excel © formula should be =MEDIAN(B2:B6) in cell C4 and copied over the range. Note that functions in ~~Excel ©~~ may vary according to ~~languages~~.		Using the median value over the window rather than the mean generates a moving median that is more robust to outliers than the mean. In such case, the Excel © formula should be =MEDIAN(B2:B6) in cell C4 and copied over the range. Note that functions in MS-Excel© may vary according to language.

			===FEM Editor 2007===
			* Denis Coulombier
			===Original FEM Authors===
			* Christophe Paquet
			* Arnold Tarantola
			* Philippe Quenel
			* Nada Ghosn
			===FEM Contributors===
			* Denis Coulombier
			* Lisa Lazareck
			* Vladimir Prikazsky

Bosmana fem: /* Describing a trend */

2022-12-18T14:46:02Z

Describing a trend

← Older revision		Revision as of 14:46, 18 December 2022
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	Figure 2: Crude data, 52 weeks moving average, and a regression line		Figure 2: Crude data, 52 weeks moving average, and a regression line

	[[File:~~Secular_trend~~.png\|600px\|frame\|none]]		[[File:secular_trend.png\|600px\|frame\|none]]


	=Describing seasonal variations=		=Describing seasonal variations=

Bosmana fem at 14:44, 18 December 2022

2022-12-18T14:44:51Z

← Older revision		Revision as of 14:44, 18 December 2022
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	Figure 1: Crude data signal		Figure 1: Crude data signal

	[[File:crudesignal\|600px\|frame\|none]]		[[File:crudesignal.png\|600px\|frame\|none]]

	The descriptive analysis of a time series aims to characterize it in terms of trends and seasons.		The descriptive analysis of a time series aims to characterize it in terms of trends and seasons.

Bosmana fem at 14:44, 18 December 2022

2022-12-18T14:44:30Z

← Older revision		Revision as of 14:44, 18 December 2022
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	Figure 1: Crude data signal		Figure 1: Crude data signal

	[[File:~~Crudesignal~~\|600px\|frame\|none]]		[[File:crudesignal\|600px\|frame\|none]]

	The descriptive analysis of a time series aims to characterize it in terms of trends and seasons.		The descriptive analysis of a time series aims to characterize it in terms of trends and seasons.

Bosmana fem at 14:43, 18 December 2022

2022-12-18T14:43:22Z

← Older revision		Revision as of 14:43, 18 December 2022
Line 4:		Line 4:
	Figure 1: Crude data signal		Figure 1: Crude data signal

			[[File:Crudesignal\|600px\|frame\|none]]

	The descriptive analysis of a time series aims to characterize it in terms of trends and seasons.		The descriptive analysis of a time series aims to characterize it in terms of trends and seasons.
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	Figure 2: Crude data, 52 weeks moving average, and a regression line		Figure 2: Crude data, 52 weeks moving average, and a regression line

			[[File:Secular_trend.png\|600px\|frame\|none]]


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	Figure 3: Crude data, and 15 weeks moving average		Figure 3: Crude data, and 15 weeks moving average

			[[File:Seasonality.png\|600px\|frame\|none]]

	Principles for calculating moving averages		Principles for calculating moving averages

Bosmana fem: Created page with "=Plotting crude data= Visual exploration of a time series uses a graphical presentation of the data plotted along a time axis. The graph must be as simple as possible to allow..."

2022-12-18T14:41:04Z

Created page with "=Plotting crude data= Visual exploration of a time series uses a graphical presentation of the data plotted along a time axis. The graph must be as simple as possible to allow..."

New page

=Plotting crude data=
Visual exploration of a time series uses a graphical presentation of the data plotted along a time axis. The graph must be as simple as possible to allow a good visual inspection of the data.

Figure 1: Crude data signal

The descriptive analysis of a time series aims to characterize it in terms of trends and seasons.

=Describing a trend=
Describing a trend requires a moving average window encompassing a full year (i.e. 52 weeks for weekly data). The shape of the resulting trend line is visually compared to the linear regression line.

Figure 2: Crude data, 52 weeks moving average, and a regression line

=Describing seasonal variations=
A moving average window of 15 weeks smoothes the crude series, highlighting the seasonal pattern of the series. The size of the moving average windows depends upon the variance of the series, corresponding to the amount of variability to be smoothed. In general, windows from 5 to 15 weeks result in appropriate smoothing, but visual inspection of the result is required.

Figure 3: Crude data, and 15 weeks moving average

Principles for calculating moving averages
Spreadsheet software such as Microsoft Excel © allows to easily display time series filtered by a moving average window. For description purposes, it is important to display the averaged value in the center of the moving average window. The example below used a five-week moving average window. The first value equals the sum of the first 5 weeks, divided by 5 (5.73). This value is plotted against week 3, which represents the middle week for this first window.

Table 1: Crude series, formulas and smoothed series for calculating moving averages in Excel (5 week window)

{| class="wikitable"
! A !! B !! C !! D
|-
| 1 || Time || Crude data || Formulas
|-
| 2 || 1 || 6.70 ||
|-
| 3 || 2 || 5.73 ||
|-
| 4 || 3 || 5.59 || 2,5
|-
| 5 || 4 || 5.15 || 3
|-
| 6 || 5 || 5.47 || 4
|-
| 7 || 6 || 6.03 || 5
|-
| 8 || 7 || 3.75 || 5,5
|}

Using the median value over the window rather than the mean generates a moving median which is more robust to outliers than the mean. In such case, the Excel © formula should be =MEDIAN(B2:B6) in cell C4 and copied over the range. Note that functions in Excel © may vary according to languages.