The ARIMA analytical method predicts future values of a time series using a linear combination of past values and a series of errors. It is suitable for instances when data is stationary/non stationary and is univariate, with any type of data pattern. It produces accurate, dependable forecasts for short-term planning, and provides forecasted values of target variables for user-specified periods to illustrate results for planning, production, sales and other factors.
The ARIMA analytical method predicts future values of a time series using a linear combination of past values and a series of errors. It is suitable for instances when data is stationary/non stationary and is univariate, with any type of data pattern. It produces accurate, dependable forecasts for short-term planning, and provides forecasted values of target variables for user-specified periods to illustrate results for planning, production, sales and other factors.
A Study on the Short Run Relationship b/w Major Economic Indicators of US Eco...aurkoiitk
The objective of this study
was to develop an economic indicator system for the US
economy that will help to forecast the turning points in the
aggregate level of economic activity. Our primary concern
is to study the short run relationship between the major
economic indicators of US economy (eg: GDP, Money
Supply, Unemployment Rate, Inflation rate, Federal Fund
Rate, Exchange Rate, Government Expenditure &
Receipt, Crude Oil Price, Net Import & Export).
ANALYSIS OF PRODUCTION PERFORMANCE OF TAMILNADU NEWSPRINT AND PAPERS LTD – C...Editor IJCATR
Every day, Tamilnadu Newsprint and Papers Ltd managers must make decisions about Production delivery without
knowing what will happen in the future. Forecasts enable them to anticipate the future and plan, many forecasting methods are
available to Tamilnadu Newsprint and Papers Ltd managers for planning, to estimate future demand or any other issues at hand.
However, for any type of forecast to bring about later success, it must follow a step-by-step process comprising five major steps: 1)
goal of the forecast and the identification of resources for conducting it; 2) time horizon; 3) selection of a forecasting technique; 4)
conducting and completing the forecast; and 5) monitoring the accuracy of the forecast. Accordingly Linear Regression method is a
widely used to predict this kind of demand. In this paper, we forecast the Production of Papers in TamilNadu Newsprint and Papers
Ltd from the past 15 years of Production using the Linear Regression method
Customer lifetime value model is based on the discounted cash flows arising from the average annual revenues contributed by each customer (model A).
The second model is also based on the discounted cash flows arising from the average annual revenues contributed by a subscriber but a constant annual growth rate is also assumed to govern the rise in the growth in revenues (model B).
The improvements to be considered include giving due consideration to estimating the future cash flows and growth rates through regression analysis, accounting for the other revenue streams that the subscriber contributes such as DTV memberships and the value of the subscriber’s social network.
A Study on the Short Run Relationship b/w Major Economic Indicators of US Eco...aurkoiitk
The objective of this study
was to develop an economic indicator system for the US
economy that will help to forecast the turning points in the
aggregate level of economic activity. Our primary concern
is to study the short run relationship between the major
economic indicators of US economy (eg: GDP, Money
Supply, Unemployment Rate, Inflation rate, Federal Fund
Rate, Exchange Rate, Government Expenditure &
Receipt, Crude Oil Price, Net Import & Export).
ANALYSIS OF PRODUCTION PERFORMANCE OF TAMILNADU NEWSPRINT AND PAPERS LTD – C...Editor IJCATR
Every day, Tamilnadu Newsprint and Papers Ltd managers must make decisions about Production delivery without
knowing what will happen in the future. Forecasts enable them to anticipate the future and plan, many forecasting methods are
available to Tamilnadu Newsprint and Papers Ltd managers for planning, to estimate future demand or any other issues at hand.
However, for any type of forecast to bring about later success, it must follow a step-by-step process comprising five major steps: 1)
goal of the forecast and the identification of resources for conducting it; 2) time horizon; 3) selection of a forecasting technique; 4)
conducting and completing the forecast; and 5) monitoring the accuracy of the forecast. Accordingly Linear Regression method is a
widely used to predict this kind of demand. In this paper, we forecast the Production of Papers in TamilNadu Newsprint and Papers
Ltd from the past 15 years of Production using the Linear Regression method
Customer lifetime value model is based on the discounted cash flows arising from the average annual revenues contributed by each customer (model A).
The second model is also based on the discounted cash flows arising from the average annual revenues contributed by a subscriber but a constant annual growth rate is also assumed to govern the rise in the growth in revenues (model B).
The improvements to be considered include giving due consideration to estimating the future cash flows and growth rates through regression analysis, accounting for the other revenue streams that the subscriber contributes such as DTV memberships and the value of the subscriber’s social network.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
2. • Using Statistics
• Trend Analysis
• Seasonality and Cyclical Behavior
• The Ratio-to-Moving-Average Method
• Exponential Smoothing Methods
• Summary and Review of Terms
Time Series Analysis and Forecasting12
3. A time series is a set of measurements of a variable that are
ordered through time. Time series analysis attempts to detect and
understand regularity in the fluctuation of data over time.
Regular movement of time series data may result from a tendency
to increase or decrease through time - trend- or from a tendency
to follow some cyclical pattern through time - seasonality or
cyclical variation.
Forecasting is the extrapolation of series values beyond the region
of the estimation data. Regular variation of a time series can be
forecast, while random variation cannot.
12-1 Using Statistics
4. A random walk:
Zt- Zt-1=at
or equivalently:
Zt= Zt-1+at
The difference between Z in time t and time t-1 is a random error.
50403020100
15
10
5
0
t
Z
Random Walk
a
There is no evident regularity in a
random walk, since the difference in
the series from period to period is a
random error. A random walk is not
forecastable.
The Random Walk
5. A Time Series as a Superposition of Two Wave
Functions and a Random Error (not shown)
50403020100
4
3
2
1
0
-1
t
z
In contrast with a random walk, this series exhibits obvious cyclical fluctuation. The
underlying cyclical series - the regular elements of the overall fluctuation - may be
analyzable and forecastable.
A Time Series as a Superposition of
Cyclical Functions
6. 12-2 Trend Analysis: Example 12-1
The following output was obtained using the template.
Zt = 696.89 + 109.19t
Note: The template contains forecasts for t = 9 to t = 20 which corresponds to years 2002 to 2013.
8. Example 12-2
Observe that the forecast model is Zt = 82.96 + 26.23t
The forecast
for t = 10
(year 2002)
is 345.27
9. 888786
11000
10000
9000
8000
7000
6000 t
Passengers
Monthly Numbers of Airline Passengers
89 90 91 92 93 94 9595949392919089888786858483828180
20
15
10
5
Year
Earnings
Gross Earnings: Annual
AJJMAMFJDNOSAJJMAMFJDNOSAJJMAMFJ
200
100
0
Time
Sales
Monthly Sales of Suntan Oil
When a cyclical pattern has a period of one year, it is usually called seasonal
variation. A pattern with a period of other than one year is called cyclical
variation.
12-3 Seasonality and Cyclical Behavior
10. • Types of Variation
Trend (T)
Seasonal (S)
Cyclical (C)
Random or Irregular (I)
• Additive Model
Zt = Tt + St + Ct + It
• Multiplicative Model
Zt = (Tt )(St )(Ct )(It)
Time Series Decomposition
11. An additive regression model with seasonality:
Zt=0+ 1 t+ 2 Q1+ 3 Q2 + 4 Q3 + at
where
Q1=1 if the observation is in the first quarter, and 0 otherwise
Q2=1 if the observation is in the second quarter, and 0 otherwise
Q3=1 if the observation is in the third quarter, and 0 otherwise
Estimating an Additive Model with
Seasonality
12. A moving average of a time series is an average of a fixed number of observations that
moves as we progress down the series.
Time, t: 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Series, Zt: 15 12 11 18 21 16 14 17 20 18 21 16 14 19
Five-period
moving average: 15.4 15.6 16.0 17.2 17.6 17.0 18.0 18.4 17.8 17.6
Time, t: 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Series, Zt: 15 12 11 18 21 16 14 17 20 18 21 16 14 19
(15 + 12 + 11 + 18 + 21)/5=15.4
(12 + 11 + 18 + 21 + 16)/5=15.6
(11 + 18 + 21 + 16 + 14)/5=16.0
. . . . .
(18 + 21 + 16 + 14 + 19)/5=17.6
12-4 The Ratio-to-Moving- Average
Method
13. 151050
20
15
10
t
Z
Original Series and Five-Period Moving Averages
• Moving Average:
– “Smoother”
– Shorter
– Deseasonalized
– Removes seasonal and
irregular components
– Leaves trend and
cyclical components
SI
TC
TSCI
MA
t
Z
Comparing Original Data and
Smoothed Moving Average
14. • Ratio-to-Moving Average for Quarterly Data
Compute a four-quarter moving-average series.
Center the moving averages by averaging every
consecutive pair and placing the average between
quarters.
Divide the original series by the corresponding moving
average. Then multiply by 100.
Derive quarterly indexes by averaging all data points
corresponding to each quarter. Multiply each by 400
and divide by sum.
Ratio-to-Moving Average
18. 180
170
160
150
140
130
120
1992F1992S1992S1992W
t
Sales
Trend Line and Moving Averages The cyclical component is the
remainder after the moving averages
have been detrended. In this
example, a comparison of the moving
averages and the estimated
regression line:
illustrates that the cyclical
component in this series is negligible.
. .Z t 155275 11059
The Cyclical Component: Example 12-3
19. The centered moving average, ratio to moving average, seasonal index, and
deseasonalized values were determined using the Ratio-to-Moving-Average method.
Example 12-3 using the Template
This displays just a
partial output for the
quarterly forecasts.
21. Example 12-3 using the Template
Graph of the Data and the quarterly Forecasted values
22. The centered moving average, ratio to moving average, seasonal index, and
deseasonalized values were determined using the Ratio-to-Moving-Average method.
Example 12-3 using the Template
This displays just a
partial output for the
monthly forecasts.
26. Z Trend Seasonal Cyclical Irregular
TSCI
MA Trend Cyclical
TC
Z
MA
TSCI
TC
SI
Z
S
TSCI
S
CTI
( )( ( )( )
( )( )
S = Average of SI (Ratio - to - Moving Averages)
(Deseasonalized Data)
Multiplicative Series: Review
27. Smoothing is used to forecast a series by first removing sharp variation, as does the
moving average.
Exponential smoothing is a forecasting
method in which the forecast is based in
a weighted average of current and past
series values. The largest weight is
given to the present observations, less
weight to the immediately preceding
observation, even less weight to the
observation before that, and so on. The
weights decline geometrically as we go
back in time.
0-5-10-15
0.4
0.3
0.2
0.1
0.0
Lag
Weight
Weights Decline as We Go BackinTime and Sumto 1
Weights Decline as we go back in
Time
-10 0
Weight
Lag
12-5 Exponential Smoothing Methods
28. Given a weighting factor: < < :
Since
So
0 1
1 1 1 1
2
2 1
3
3
1 1 2 1
2
3 1
3
4
1 1 1 1
2
2 1
3
3
w
Zt w Zt w w Zt w w Zt w w Zt
Zt w Zt w w Zt w w Zt w w Zt
w Zt w w Zt w w Zt w w Zt
( ) ( )( ) ( ) ( ) ( ) ( )
( ) ( )( ) ( ) ( ) ( ) ( )
( ) ( )( ) ( ) ( ) ( ) ( )
Zt 1 w(Zt ) (1 w)(Zt )
Zt 1 Zt (1 w)(Zt - Zt )
The Exponential Smoothing Model