HTime series using Holt-Winters Forecasting Procedure
Summary
The Holt-Winters forecasting procedure is a simple widely used projection method which can cope with trend and seasonal variation. We can apply this method to lots of fields such as banking data analysis, investment forecasting, inventory controlling and so on. This paper shows us a practical banking credit card example using Holt-Winter method in Java programming for data forecasting. The reason we use Holt-Winter is that this method is simple while generally works well in practice, and is particularly suitable for producing short-term forecasts for sales or demand time-series data. Theorem

There are two types of seasonal model: an additive version which assumes that the seasonal effects are of constant size and a multiplicative version which assumes that the seasonal effects are proportional in size to the local deseasonalized mean level. Both seasonal models assume that the local deseasonalized mean level may be modified by an additive trend term and also that there is an additive error term of constant variance. Suppose we have an observed time series, denoted by X1, X2, …, Xn , and wish to forecast Xn+k. The forecast made at time n for k steps ahead will be denoted by Xnk. For a univariate forecast this depends only on Xn, Xn-1,…… In simple exponential smoothing, the one-step-ahead predictor can be written in the recurrence form Xt(1)= Lt+ Tt+ It-p+1

Where the smoothing parameter, α, is usually constrained so that 0 < α <1. The Holt-Winters method (sometimes called the Winters method or seasonal exponential smoothing) generalizes this approach to deal with trend and seasonality. Let α, γ, δ denote three smoothing parameters and let p denote...

...TIMESERIES ANALYSIS
Introduction
Economic and business timeseries analysis is a major field of research and application. This analysis method has been used for economic forecasting, sales forecasting, stock market analysis and company internal control. In this paper, we will talk about timeseries and review techniques that are useful for analyzing timeseries data.
Definition of TimeSeries and TimeSeries Analysis
Timeseries is an ordered sequence of values of a variable at equally spaced time intervals. Timeseries data often arise when monitoring industrial processes or tracking corporate business metrics.
The analysis of timeseries is based on two basic assumptions. One is successive values in the data file represent consecutive measurements taken at equally spaced time intervals. The other assumption is that time is the only one independent variable in timeseries function.
Applications of TimeSeries Models
• Identify the nature of the phenomenon represented by the sequence of observations, and
• Fit a model and proceed to forecasting, monitoring or even feedback and feedforward control....

...Timeseries
In statistics, signal processing, econometrics and mathematical finance, a timeseries is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of timeseries are the daily closing value of the Dow Jones index or the annual flow volume of the Nile River at Aswan. Timeseries analysis comprises methods for analyzing timeseries data in order to extract meaningful statistics and other characteristics of the data. Timeseries forecasting is the use of a model to predict future values based on previously observed values. Timeseries are very frequently plotted via line charts.
Timeseries data have a natural temporal ordering. This makes timeseries analysis distinct from other common data analysis problems, in which there is no natural ordering of the observations (e.g. explaining people's wages by reference to their education level, where the individuals' data could be entered in any order). Timeseries analysis is also distinct from spatial data analysis where the observations typically relate to geographical locations (e.g. accounting for house prices by the location as well as the...

...TimeSeries Analysis: The Multiplicative Decomposition Method
Table of Contents
Page
Abstract………………………………………………………………………………………………………………………………………….3
Introduction………………………………………………………………………………………………………………………...…4-5
Methodology: Multiplicative Decomposition……………………………………………….…5-7
Advantages/Disadvantages of Multiplicative Method………………………………7-8
Conclusion…………………………………………………………………………………………………………………………………..8
Abstract
One of the most essential pieces of information useful to compute sales, and the ability to forecast them is strategically important. Forecasts can provide useful information to cut costs, increase efficient use of resources, and improve the capability to compete in a frequently changing environment. This study tests complicated, yet simple to use timeseries models to forecast sales. The results will show that, with minor rearrangement of past sales data, easy-to-use timeseries models can accurately forecast gross sales .Forecasters often need to guesstimate doubtful quantities, but with restricted time and resources. Decomposition is a method for dealing with such problems by breaking down the estimation task down into a set of components that can be more readily estimated, and then combining the component estimates to...

....2.3 Timeseries models
Timeseries is an ordered sequence of values of a variable at equally spaced time intervals. Timeseries occur frequently when looking at industrial data. The essential difference between modeling data via timeseriesmethods and the other methods is that Timeseries analysis accounts for the fact that data points taken over time may have an internal structure such as autocorrelation, trend or seasonal variation that should be accounted for. A Time-series model explains a variable with regard to its own past and a random disturbance term. Special attention is paid to exploring the historic trends and patterns (such as seasonality) of the timeseries involved, and to predict the future of this series based on the trends and patterns identified in the model. Since timeseries models only require historical observations of a variable, it is less costly in data collection and model estimation.
. Timeseries models can broadly be categorized into linear and nonlinear Models. Linea models depend linearly on previous data points. They include the autoregressive (AR) models, the integrated (I) models, and the moving average (MA)...

...Forecasting Models: Associative and TimeSeries
Forecasting involves using past data to generate a number, set of numbers, or scenario that corresponds to a future occurrence. It is absolutely essential to short-range and long-range planning.
TimeSeries and Associative models are both quantitative forecast techniques are more objective than qualitative techniques such as the Delphi Technique and market research.
TimeSeries Models
Based on the assumption that history will repeat itself, there will be identifiable patterns of behaviour that can be used to predict future behaviour. This model is useful when you have a short time requirement (eg days) to analyse products in their growth stages to predict short-term outcomes.
To use this model you look at several historical periods and choose a method that minimises a chosen measure of error. Then use that method to predict the future. To do this you use detailed data by SKU's (Stock Keeping Units) which are readily available.
In TSM there may be identifiable underlying behaviours to identify as well as the causes of that behaviour. The data may show causal patterns that appear to repeat themselves – the trick is to determine which are true patterns that can be used for analysis and which are merely random variations. The patterns you look for include:
Trends...

...TIMESERIES ANALYSIS
Chapter Three
Univariate TimeSeries Models
Chapter Three
Univariate timeseries models c WISE
1
3.1
Preliminaries
We denote the univariate timeseries of interest as yt.
• yt is observed for t = 1, 2, . . . , T ;
• y0, y−1, . . . , y1−p are available;
• Ωt−1 the history or information set at time t − 1.
Call such a sequence of random variables a timeseries.
Chapter Three
Univariate timeseries models c WISE
2
Martingales
Let {yt} denote a sequence of random variables and let It =
{yt, yt−1, . . .} denote a set of conditioning information or information
set based on the past history of yt. The sequence {yt, It} is called a
martingale if
• It−1 ⊂ It (It is a ﬁltration)
• E [|yt|] < ∞
• E [yt|It−1] = yt−1 (martingale property)
Chapter Three
Univariate timeseries models c WISE
3
Random walk model
The most common example of a martingale is the random walk model
yt = yt−1 + εt,
εt ∼ W N (0, σ 2)
where y0 is a ﬁxed initial value.
Letting It = {yt, . . . , y0} implies E [yt|It−1] = yt−1 since E [εt|It−1] = 0.
Chapter Three
Univariate timeseries models c WISE
4
Law of Iterated Expectations
Deﬁnition 1. In general, for information sets It and...

...TimeSeries Models for Forecasting New One-Family Houses Sold in the United States
Introduction
The economic recession felt in the United States since the collapse of the housing market in 2007 can be seen by various trends in the housing market. This collapse claimed some of the largest financial institutions in the U.S. such as Bear Sterns and Lehman Brothers, as they held over-leveraged positions in the mortgage backed securities market. Credit became widely available to unqualified borrowers during the nineties and the early part of the next decade which caused bankers to act predatorily in their lending practices, as they could easily sell and package subprime mortgage loans on leverage. This act caused a bubble that would later burst when unqualified homebuyers began defaulting on their loans causing a tremendous downfall in the U.S housing market. Understanding which direction key market factors, such as the housing market, are going can help re-establish stability in the market, which is at an all-time premium. This paper is designed to help better predict the direction of the housing market in the future via the use of timeseries models, in an effort to re-establish a sense of stability in the housing market.
The Data Pattern of New One-Family Houses Sold in the U.S.
The following chart (Figure 1) represents the timeseries data for non-seasonally adjusted home...

...TIMESERIES MODELS
Timeseries analysis provides tools for selecting a model that can be used to forecast of future events.
Timeseries models are based on the assumption that all information needed to generate a forecast is contained in the timeseries of data. The forecaster looks for patterns in the data and tries to obtain a forecast by projecting that pattern into the future.
A forecasting method is a (numerical) procedure for generating a forecast. When such methods are not based upon an underlying statistical model, they are termed heuristic.
A statistical (forecasting) model is a statistical description of the data generating process from which a forecasting method may be derived. Forecasts are made by using a forecast function that is derived from the model.
WHAT IS A TIMESERIES?
A timeseries is a sequence of observations over time.
A timeseries is a sequence of data points, measured typically at successive time instants spaced at uniform time intervals.
A timeseries is a sequence of observations of a random variable. Hence, it is a stochastic process. Examples include the monthly demand for a product, the annual freshman...