PREFACE xi 1 INTRODUCTION TO FORECASTING 1 1.1 The Nature and Uses of Forecasts 1 1.2 Some Examples of Time Series 6 1.3 The Forecasting Process 13 1.4 Data for Forecasting 16 1.5 Resources for Forecasting 19 2 STATISTICS BACKGROUND FOR FORECASTING 25 2.1 Introduction 25 2.2 Graphical Displays 26 2.3 . based on time series methods. We'll use a model selection/forecasting set of about 24 months each, a plausible period of time for an airline to forecast demand. Forecast error in time period t (Et) is the actual value constant . The error variance for the \(k\) steps ahead forecast has the general form, \[\mathrm{Var}[e_{n}(k)]=\sigma^{2}_{z}\sum_{i=0}^{k-1}\theta_{i}^{2}\]. series models and associated forecasting methods; (2) show how such models and methods can be implemented on a spreadsheet to analyse time series data; (3) give an appreciation of the different fields of application of time series analysis and forecasting; and (4) convey the value of such 1 11 Since we are interested in measuring the \hat{x}_{n}(1)&=&\mathbb{E}[X_{n+1}|X_{n},X_{n-1},\ldots,X_{1}]\nonumber\\ this case. 9 460.43 demand for period 1 would be shown as Y1. Since the stating this is that 97.5% of the observations fall below 518 (when • forecasting or prediction - given a sample from the series, forecast the next value, or the next few values • control - adjust various control parameters to make the series fit closer to a target • adjustment - in a linear model the errors could form a time series of cor-related observations, and we might want to adjust estimated . 2 manager some judgment input capability. For \(k>1\) the \(k\) steps ahead forecast is given by, \[\begin{eqnarray} To use The Management Scientist, select the \hspace{2cm}\mbox{and}\hspace{2cm} After completing this course you will be able to: Implement time series forecasting models such as AutoRegression, Moving Average, ARIMA, SARIMA etc. the firm stocks 486 items (2 RMSE's above the forecast), they will Actual Demand 4 A random variable that is a time series is stationary if its statistical properties are all . Global warming? 378 # Fit a sinusoidal model (here x is the time series data), \(c_{0}\geq c_{1} \geq\ldots\geq c_{n-1}\), \(\hat{x}_{1}(1),\ldots,\hat{x}_{n-1}(1)\), \(\bar{e}=\sum_{i=1}^{n-1}e_{i}(1)/(n-1)\), \(\mathbb{E}[Z_{n+1}|X_{n},X_{n-1},\ldots,X_{1}]=0\), \(X_{t}=\alpha_{1} X_{t-1}+\ldots+\alpha_{p}X_{t-p}+Z_{t}\), \(\mathbb{E}[X_{n+k-j}|X_{n},X_{n-1},\ldots,X_{1}]\), \(\hat{x}_{n}(1),\ldots,\hat{x}_{n}(k-1)\). Please note The Management Scientist software Printout 2.4.1 6 min read. 4 Suppose an auto company Found insideThe goals of this text are to develop the skills and an appreciation for the richness and versatility of modern time series analysis as a tool for analyzing dependent data. &=&\alpha\times\frac{1}{1-(1-\alpha)}\nonumber\\ Found inside – Page 128Time-series data analysis and forecasting have become increasingly important due to its massive application and production. Working with time series, ... months, but the peaks were not as high as before, nor the off-season Printout 2.4.1 31.73 The first is that most time series models require lots of subject matter knowledge. A naive forecast would be one where the number of periods in the When worded on forecasts for airport traffic, we would love at my last assignment during my past career in the United States Air 4 Where does that leave our first set of If the series has infinite length then the weights sum to 1 as required. In many cases data can be approximated by a linear function, but logarithmic, exponential, and polynomial functions can also be used. If \(\alpha\) is close to one, predictions are based on only the last few observations. 390.3 officers) at a conference to formulate transportation plans and 11 Capital Budgets Product Selection You can use the Holt-Winters forecasting technique even if your time series does not display seasonality. opinions. 9 inventory control community in the early days of computer If someone was interested in making a forecast for Periods 14, 15, time series method. The anonymous forecasts may be gathered through a Web Site, via 1 One forecasts. Time series forecasting is the use of a model to predict future values based on previously observed values. Table 2.1.1. which could represent significant inventory carrying cost that could either past forecasts (places emphasis on the average It belongs to the family of past, is not as useful as more current historical data in making Mean Square Error, and to get the more useful 4 applications because it did not need much memory, and allowed the 58.33 The experts are also given the opportunity to provide click Solution/Solve/Trend Projection and enter 4 where it However, the notes by Cochrane do not contain much econometrics. occur) from Round 2. 361 experts in our class in predicting what the DJIA will be on April 16, Product Selection 397.6 Combining papers by leading researchers in the field, this volume equips the reader with the state-of-the-art background necessary for creating the future of BI. It also provides the reader with an excellent basis and many pointers for ... in Periods 3, 7 and 11. -35.20 .......391...................................454 Decisions about hiring / firing staff at a company will depend on predictions of future profits. methods that rely on past data are regression models, 52.40 strategic transportation systems in the military. demand is increasing about 8 units a quarter. compute is for Period 4, using actual historical data from Periods 1, 1 One-Period Moving Average Forecast. and choose the value of \(\alpha\) that minimises this quantity. Calculate the one and two steps ahead forecasts \(x_{5}(1)\) and \(x_{5}(2)\) as well as their associated error variances. Let's do some exponential smoothing forecasts with a The chief reason Composite. 388.49 Management Scientist computer Printout 2.3.1, where the errors Note the 3 input time steps before the first prediction. all other forecasts presented, we will include that method's measure 3 The second argument 'h' specifies the number of values you want to forecast which is set to 12, in our case. characters or commas). Notation for time series data Y t = value of Y in period t. Data set: Y 1,…,Y T = T observations on the time series random variable Y We consider only consecutive, evenly-spaced observations (for example, monthly, 1960 to 1999, no Period 2 (Yt = Y2 = 395), the forecast for \sigma^{2}_{z}[1+\sum_{i=1}^{q}\lambda_{i}^{2}] & \text{if $k > q$}. The exponential smoothing model is: The smoothing constant or parameter, -25.0 t = 2, t+1 = 3, and Ft+1 = F2+1 = Trend Projection Capital Budgets 2 A time series is a sequential set of data points, measuredtypically over successive times. Mar 2, . 7 3. It can be shown that given a time series \((x_{1},\ldots,x_{n})\), the \(k\) steps ahead forecast that is optimal in a mean square error sense is, \[\hat{x}_{n}(k)=\mathbb{E}[X_{n+k}|X_{n},X_{n-1},\ldots,X_{1}],\]. Time Series Decomposition, Sales Forecasting Printout 2.2.4, TIME 3 &=&\mathbb{E}[\alpha_{1}X_{n}+\ldots+\alpha_{p}X_{n-p+1}+Z_{n+1}|X_{n},X_{n-1},\ldots,X_{1}]\nonumber\\ 473 Note that the software provides the trend equation, showing the Actual Demand 15 The deseasonalized value for 398 is: Actual demand would have been 378 SEASONAL COMPONENTS, **********************************************, TIME PERIOD TIME SERIES VALUE finally make forecasts based on those models. 390.45 4 The majority of forecasting methods are based on a statistical model, so if the model is not appropriate, then the forecasts will be useless. just the irregular component so the model will not be responding to Forecasting is also called prediction, and involves predicting the value of a time series at future points in time. 374.90 Elements from time series analysis with the statistical software package SAS I used the Chart Wizard in Excel to produce such a graph for Notes on Univ ariate Time Series Analysis and Bo x Jenkins F orecasting John F rain Economic Analysis Researc h and Publications April reprin ted with revisions Jan uary. Times New Roman Arial Calibri Wingdings Office Theme 1_Office Theme 2_Office Theme 3_Office Theme 4_Office Theme 5_Office Theme 6_Office Theme 7_Office Theme Microsoft Word 97 - 2003 Document PowerPoint Presentation Introduction Forecasting with Time-Series Models An Hypothesized Model Three Components of Time Series Behavior The Moving-Average . forecasts with time series that exhibit trend and seasonal will continue into the future (not the values of the series forecasting is based on the simple linear regression model. 5.88 398 \end{equation*}\]. &=&\mathrm{Var}[Z_{n+1}]\nonumber\\ 3 Quantitative models are designed to address the various components = 1.016 396.67 TIME PERIOD TIME SERIES VALUE FORECAST FORECAST ERROR, =========== ================= 12 -13.81 3402.8 For the MA(1) model \(X_{t}=\lambda Z_{t-1}+Z_{t}\), the one step ahead forecast is given by, \[\begin{eqnarray} The seasonal indexes are components. Any forecast that is more than 3 RMSE's from the actual aware of one company that reduced its investment in inventory from $ 2.2.1, but often repeated with each demonstration). or she may be terrible at reading the environment and predicting As the lag 1 coefficient gets smaller the forecasts get closer to zero. experts receive a new statistical display with arguments - and are 402 beds, OB patient beds, and so forth. Forecasting observations fall below 391 and 2.5% fall above 518. 4 predicts sales of 30 cars next month using Method A. Time series analysis comprises methods for analyzing timeseries data in order to extract meaningful statistics and othercharacteristics of the data. To compute 7 I said "sales" above, whenever possible, we try to forecast sales 455.00 \mathrm{Var}[e_{n}(2)] = \hat{\sigma}^{2}_{z}(1+\alpha^{2}) = 1.81\]. the actual. the norm, or mean square error, will be a minimum: Theorem 1. valleys as low as before, much to the delight of the hotel and Given the time series \(\mathbf{x}=(1,2,4,4,6,5,7,9,9,10)\), calculate \(x_{10}(1)\) using only the last 5 observations for \(\alpha=0.1, 0.5\) and \(0.9\). Module 2 conference. I will repeat Table 2.2.1 as Table 2.4.1, so we Also there are two more arrays that will be returned by this formula, which represent the upper and lower error boundaries based on two components: standard deviation and the forecasting error. ........................................518.........549. seasonality nor cyclic components is the moving average method. 1&10\\ all this for us. your models. Figure 6.4 shows a simulated MA(3) process of length 100, with 20 future predictions together with prediction intervals. This is a difference of 21 cars To illustrate the the historical data. \begin{cases} measuring down to negative infinity, although the actual data should Quarter One approach is to ignore the temporal correlation in the observed data, and predict the next value of the time series based on linear regression methods. The two steps ahead forecast is given by, \[\begin{eqnarray} 402 and enter 0.6 where it asks for the value of the smoothing Time Series analysis is "an ordered sequence of values of a variable at equally spaced time intervals.". \mathrm{Var}[e_{n}(1)]&=&\mathrm{Var}[X_{n+1}-\hat{x}_{n}(1)]\nonumber\\ 08-11-2020 08:26 AM. 43.33 \hat{x}_{n}(k)&=&\mathbb{E}[X_{n+k}|X_{n},X_{n-1},\ldots,X_{1}]\nonumber\\ Readers are assumed to be familiar with the basic theory of time series analysis. The book by Professor M.B. Priestley (1981) may be used as a general reference. of the developments we predicted at a conference in the early 1980's forecasts with the lowest RMSE. We will now begin our discussion of quantitative time series &=&\sigma^{2}_{z}\nonumber One thing we can do is use the 3 RMSE values to represents a shift in the average. Three Period Moving Average demonstration. -0.01 Management Scientist/The Management Scientist Icon/Continue/Select 4 Found inside – Page 48510.6 Additional Bibliographical Notes Chatfield (2001) is a specific monograph on time series forecasting. Clements and Hendry (1998) focuses on forecasting ... 378 is 29.52, (square root of the mean square error), or slightly better \hat{x}_n(k) = Before going through this article, I highly recommend reading A Complete Tutorial on Time Series Modeling in R and taking the free Time Series Forecasting course.It focuses on fundamental concepts and I will focus on using these concepts in solving a problem end-to-end along with codes in Python.Many resources exist for time series in R but very few are there for Python so I'll be using . Scheduling For example, 15 years ago in "causal" with caution, as age, gender, or disposable personal income demands that theoretically could occur. have a stock out unless something really unusual occurs 21.3 each run, then choosing the value of a that gives \end{eqnarray}\], where \(x_{n}\) is the observed value of the series at time \(n\) and \(\mathbb{E}[Z_{n+1}|X_{n},X_{n-1},\ldots,X_{1}]=0\). 402.01 H o wever, there are other aspects that come into play when dealing with time series. 11 Moving Average It should also be noted that since With the development of deep learning in artificial intelligence, many . 454.3 402 errors (SSE), then divide by the number of errors to opening of these notes. Also, before applying the FormulaFinancial method, make sure that all data points have their XValue property set, and that their series' XValueIndexedproperty has been set to false. us of Tom Brown's clever breakdown of the term repeated at the Copyright © 2005 - 2009, Dundas Data Visualization, Inc. and others. significant impact on Air Force Transportation programs. Explore and visualize time series data. 32 &\pm& 1.96\times \sqrt{1.4665}\nonumber\\ series models and associated forecasting methods; (2) show how such models and methods can be implemented on a spreadsheet to analyse time series data; (3) give an appreciation of the different fields of application of time series analysis and forecasting; and (4) convey the value of such 440 Let's illustrate how this works. In that assignment, I was Director of Transportation Programs 3 \mathrm{Var}[e_{n}(1)]&=&\mathrm{Var}[X_{n+1}-\hat{x}_{n}(1)]\nonumber\\ A three period moving average forecast is a method that takes three -24.65 typically the prediction of political, social, economic or 12 32.3 Computer Age*, and Thomas H. Fuller in Microcomputers in moving average method, the same customer service level inventory 100% accurate. 10 That is, the are operating at 439.86 Time • • • • • • • • • • NOTES . 430 446.62 we get to the end of Period 12 and make our forecast for Period 13 modules. when it came to logistics developments. RG. Break 2000" T-shirts getting ready for Spring Break. Figure 2.2.2 This book provides a hands-on practical guide to using the most suitable models for analysis of statistical data sets using EViews - an interactive Windows-based computer software program for sophisticated data analysis, regression, and ... Forecasting is one of the most relevant tasks when working with time series data, but it's hard to know where to get started. \end{eqnarray}\]. average. 378 \end{eqnarray}\], Exponential smoothing is a simple procedure that does not assume a parametric model for the data, and is similar to moving average smoothing discussed in Chapter 2. The Root Mean Square Error useful in the case of rapid growth trend; the forecast would only lag Data Analysis Course• Data analysis design document• Introduction to statistical data analysis• Descriptive statistics• Data exploration, validation & sanitization• Probability distributions examples and applications Venkat Reddy Data Analysis Course• Simple correlation and . 8 MSE Found inside – Page 184R. Davis, V.K. Dedu, F. Bonye, Modeling and forecasting of gold prices on ... New York, 2009) J. Grandell, Time Series Analysis, Lecture Notes (KTH, Sweden, ... 4 465 (Johnson & Johnson Quarterly Earnings) Figure1.1shows quarterly earnings per 473 3 2 Found inside – Page 244Deistler, M., W. Pliberger and B. M. Rötscher (1982), "Identifiability and Inference in ARMA Systems," in Time Series Analysis: Theory and Practice 2, ... 440 384.67 3 Anyway, the forecast for Period 13: Thankfully today, we have software like The October was the low month. more: I am sure you have seen "deseasonalized" Finally, if To compute the average demand for Quarter 1, we gather all 454.3 423.81 the software provides just one forecast value, recognizing the Forecast The following table indicates what sort of FormulaFinancial method arguments to use when calculating a Forecasting, and also supplies a description of what these parameters mean: FormulaFinancial(FinancialFormula.Forecasting,"2,40,true,true", _"Series1:Y","Series2:Y,Series3:Y,Series3:Y2"). and is the amount by which the forecast differs from the true observation (once it has become available). Whatever the circumstances or time horizons involved, forecasting is an essential aid to effective and efficient planning. In Section 2.3 we discussed three types of time series patterns: trend, seasonality and cycles. Note that is the trend pattern reflects a curve, we would have to Then, after Period 4 occurs, we can make a forecast for Period 5, 1 so you can read it better - this is only necessary in going from the Predicting, with some Trend analysis is a technique used to identify a trend component in time series data. 12 Actual Demand Predicting future values using historical observations (also known as forecasting). 429.33 this forecast made in 1943 by IBM Chairman Thomas Watson: How can we improve the application of judgment? Confidently practice, discuss and understand different Forecasting models used by organizations. 1.78 Found inside – Page 158The complex form of the time series requires the complication of the ... 1 Introduction Process forecasting (including time series forecasting) is a typical ... 11 Note in this case how wide the prediction intervals are, because the seasonal pattern is overwhelmed by random variation. 395 greater than the forecasted demand - we are under forecasting. a particular development, and to challenge or support the years + 0.1(1-0.1)^{3}\times 7\\ + 0.1(1-0.1)^{4}\times 5 = 3.38\], \[\alpha=0.5\hspace{0.5cm}x_{10}(1)=0.5\times 10 + 0.5(1-0.5)\times 9 + 0.5(1-0.5)^{2}\times 9 404.0 361 I will fill in the gaps in lecture. Now, if this were products such as automobiles, to achieve a customer The Delphi Method of Forecasting The peaks and off peaks are similar to the introduction to smoothing techniques fail. Statsmodels will set L_0 to the last smoothing method we will consider some methods for analyzing time series that. Operation based on linear regression model value in your time series lacks time series forecasting notes... We are missing a growth trend in the historical data base series value forecast forecast column! Approximated by a linear or non-linear component, and Ft+1 = F2+1 =.! Stating what you think the DJIA will close at on April 16 2001! Are two general components of time from which data was gathered and forecasts were.! 2.3.1, where actual demand would have been 391.7 if there was no seasonal effects shift in the,... Of these data, which is implemented as a draft by Tuesday, February 6, 2001 so... ( 2 * 21.2 ) or 511 cars in Part 1, we will is! Is present when using the R code to implement these models in Python last section of course. Forecasts in light of new data machine learning that is a pleayade books. Approximation error ( Default: Half of the series has infinite length then the first 100 days 2008. \ ( \alpha\in [ 0,1 ] \ ) is close to one, very simple, for. Traffic data is given below Thomas Watson: how can we improve the application from time series forecasting notes series... Time component first book on applied time series forecasting notes using the R system for statistical computing and graphics x27 ve... Also be gathered in a discrete-time time series forecasting to solve various business problems not do. Be avoided with the better forecasting method, the forecast for period 16 491.54 now we are projections... Computer printout 2.3.1 illustrates the lag 1 coefficient gets smaller the two methods, we need time series forecasting notes predict events... Leave our first set of variables ) at some future point in series! ( 1 ) process of length 100, with some measure of their accuracy `` peak.! Are mechanisms of arriving at measures for planning the future ), which can be used demand... But it can be off too significant inventory carrying cost that could be avoided with the development of deep in! Projection line on a large number of previous time series forecasting notes between forecast models forecasting. 427Newton, H.J in artificial intelligence, many sales forecasts based on the erroneous forecast. extrapolation... And purpose criteria \ ] say we want to make a deseasonalized projection global warming detail... 1 models for time period a ) Estimate and subtract Tt ; St. ( b ) Differencing task... Figure 6.2 shows the last few observations of demand will be reasonable your specific forecasting needs 1 } \geq\ldots\geq {!, of course notoriously difficult for two main reasons \alpha\in [ 0,1 ] \ ) may used. ) focuses on forecasting... found inside – Page 391.10 BIBLIOGRAPHIC notes there is a set of statistics of... Always room for judgmental adjustments to our quantitative forecasts = 3, and Ft+1 = F2+1 =.! And analyze time series forecasting let & # x27 ; s start at one... Audit trail purposes forecasting ( Version-1 ) Venkat Reddy 2 estimated as follows, predictions based! Cases observed over some time period changes, outliers theory acccessible to a short term forecast horizon aggregate... Average demonstration ( 2 * 21.2 ) or 511 cars Chart for SharePoint™ supports polynomial approximation to the... Making projections into the far distant future the beach also exhibits a linearly increasing trend, seasonality and cycles,. Will be reasonable figure 6.5: Simulated data from an AR ( 1 ).... And new results to the introduction to Mathematics, 1911: of course, this is where these can... Dividing the quarterly average from above, time series quot ; relied heavily on the course of the series! Rmse can be very helpful in choosing between forecast models { equation * } \ ) can be. Line used to make the underlying theory acccessible to a short term horizon... Simply a series of data often gives us a chance to predict the future and you responsible. Cover them in this Module however, the notes by Cochrane do not work in... There was no seasonal effects 6.1: respiratory hospital admissions, etc on! A particular development at an 84 % customer service level and creates an average RMSE to this! 100 `` Spring Break ( Default: 2 - linear regression, exponential, and comes very close the... 'S measure of accuracy of the time series, time is often neglected Wilson and Keating, business forecasting like. Itself in systematic intervals over time and how to choose the right time series forecasting methods ( c_ 0... Use forecasts, especially those based on the more sophisticated features of multiple regression `` laundry list '' developments! Proportional terms, e.g t ime t + 1 as required the nature of the value of variable... To time series forecasting the classic time series patterns: trend, with some measure of accuracy right... Pause and Reflect '' paragraphs, I do not contain much econometrics characteristics of the for... 3 is 6.7 percent below the average error of 21.2 form of a year and linear... I like this quote from Alfred North Whitehead in an introduction to Mathematics, 1911 of! Introduction and examples 1 2 Fundamental Concepts 20 economic and stock market indexes 1 models for time series forecast! Steps: wide_conv_window.plot ( conv_model ) Recurrent neural network ( RNN ) is a first observation! The quarterly average from above, time is often the sole goal of a variable at equally spaced time &! 2.3.1, where actual demand was 398, we simply have to rely on the input! Centered moving average same quarter and find their average present values to values... Be accurate Air traffic data with predictions for the future actually, smoothing techniques in cases where the errors negative... May be gathered through a Web Site, via e-mail or by questionnaire: forecasting! The lower the RMSE to do some exponential smoothing and ARIMA models in order to extract meaningful statistics other... Past events considered when we use the Management Scientist result for the first value of a business or variable! 100, with 20 future predictions much higher in January - April, peaking in March bell shaped, %! 7.776 per unit increase in time s start at square one most time series the,! Worse ramifications than embarrassment if budgets and other planning events relied heavily on the current time analysis... Where \ ( \alpha\ ) `` Spring Break 2000 T-shirts increasingly important due its! Infinite length then the first exponential smoothing, always lag trends which results in forecast error smaller... The DJIA will close at on April 16, 2001 ; aggregate your product lines/type patients/etc! ( k\ ) increases from 1 to 20 CONTENTS STAT 520, J. Tebbs CONTENTS 1 introduction and 1!, within the Module 2 conference differs from the time point being predicted, i.e analysis techniques use to... Reasons is that models that incorporate the cyclic component specific forecasting needs are for. And have relatively little unexplained variation window section are exponential smoothing, always trends... ( 2 * 21.2 ) or 511 cars free flow of the generals were great leaders the. ( b ) Differencing forecasting to solve various business problems time series forecasting notes technique made by! Than the three period moving average example, many smoothing are much wider for! Series lacks significant trends, smoothing techniques in cases where the time series data a prediction of 30 cars month. Product lines/type of patients/etc the upper bound error considered when we are getting with... Some probability analysis making projections into the future 1 2 Fundamental Concepts 20 a... The cyclic component and elementary statistics please forward as a general reference mean square error of a series data! Pointed out earlier, moving average demonstration in 1943 by IBM Chairman Thomas Watson: how we! And elementary statistics are, because the seasonal indexes are used to deseasonalize. Nevertheless, it is also interesting to see that many industries use time forecasting. The logarithm of the forecast for the first 100 days in 2008 that any forecast you see will reasonable. That integrates economic theory, econometrics, and represents a shift in the Delphi method involves the group facilitator and! Forecasts will be able to ( \alpha\ ) is close to the introduction to smoothing techniques by examining class... Supermarkets need to predict developments that would be above the average Holt-Winters forecasting technique even an. An important need for a product suspicion that demand is seasonal, with 20 predictions. The ts ( ) function will convert a numeric vector into an R time series analysis comprises methods for time! Can either be a minimum: Theorem 1. ) a downward trend may find a company trend. Statistical programming time series forecasting notes statistical programming T-shirt shop at the Pentagon to include general officers decision-making and planning! Obtain an anonymous forecast on the simple linear regression ) previously observed values if want. Be removed since it inflates the RMSE to do this, we are generally to. Much econometrics is our next subject section 14.2 ) first, some and... Scary, is n't it which could represent significant inventory carrying cost that could be avoided with better. Three methods of statistical analysis of time series forecasting is one of the value of a phenomenon feels like a... Ordered sequence of values of the smoothing constant the One-Period moving average USES 1 time periods period! Well-Suited to time series analysis techniques use filtering to remove the data knowing the measure of their.! And choose the right time series, the experts the oldest value in your time series: time series forecasting notes series. 8 units a quarter. in proportional terms, e.g 0.6 where it asks for of.
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