Journal "Annals – Economy Series", No. 16 / 2013
SIMPLE MOVING AVERAGE VS LINEAR REGRESSION FORECAST
Lecturer Nicolae Adrian MATEIA, PhD "Dimitrie Cantemir" Christian University Faculty of Management in Tourism and Commerce Timişoara, Romania E-mail: [email protected]
Abstract: To determine and characterize the components that exist in a time series, it is advisable to make a valid prediction of future evolution. Characterization and description of the trend can be done using statistical methods (simple) or analytical. In choosing a method an important role has the statistical chart and how to discover the existence and shape of the various components of a time series representation. The purpose of this paper is to find a more accurate way of predicting the future evolution, based on moving averages and linear regression function.
Keywords: moving average, linear regression, trend
JEL Classification: C00, C53.
1. Introduction The analysis of foreign exchange market involves studying the factors that influence market development and formation of a new currency. Thus, there are three basic types of market analysis: Fundamental analysis–studying fluctuations in exchange rates under the influence of economic and political factors in order to determine the common trend of market development. This analysis is used primarily when dealing with long-term strategies based on the trends for several months or years. Analysis of core and their relationship determines the main trend right from the beginning of its cycle of existence. In
83 Journal "Annals – Economy Series", No. 16 / 2013 order to assess the optimal timing for initiating the transaction it’s not enough fundamental analysis. Technical analysis- it deals with the study of technical factors, with the use of financial and mathematical instruments. Technical analysis allows visual identification of the trend and the fundamental analysis explains the reasons of existence and continuity of these trends. Intuitive Approach – it cannot be called pure analysis, given that it involves the study of the psychological factors which cannot be analyzed in the form of quantitative measurements, and this means that neither their dynamics can not be analyzed. This approach comes rather to complete fundamental and technical analysis.
2. Moving average vs linear regression Moving average (SMA) method is used especially when the time series has regular fluctuations (seasonal or cyclical) for a smooth evolution of the phenomenon. Long-term trend is determined as averages calculated of as many terms (m) to how many a complete oscillation occurs. Environments are called mobile, sliding, as permanently in the calculation of such average the first term of the previous average is left out and the next term is entered. Thus, if the moving averages are calculated, for example, of five terms, each adjusted amount shall include the term of the respective period, the two previous terms and the two subsequent terms. y y y y y y t2 t 1 t t1 t 2 , tn3, 2 . tTMM 5 In general, if the averages are calculated from m terms (m- odd) they will be lost by calculating averages, (m - 1) terms and each adjusted value will stand to a value lying recorded. However, if the moving averages are calculated from m terms (m- even number), then the mean is between the real terms and we will center levels, thus adjusted, by calculating the average’s average (partial). In this case m terms will be lost by centered calculating averages. By calculating moving averages, seasonal deviations are compensated.
84 Journal "Annals – Economy Series", No. 16 / 2013
Let us note that moving averages can also be calculated where there are no regular diversions in order to remove residual variations. As the moving averages are being calculated from a larger number of terms, more accentuated will be its smoothness; on the other hand, calculating averages of a shortage of terms it can make it impossible to eliminate residual variations from the actual values. Simple linear regression(Forecast) assumes that the economic phenomenon Y (the effect phenomenon) is the result of a main factor X and of some factors with random actions considered nonessential, specify by the variable residual „ ”: xfy )( The probabilistic linear model for the variable Y-effect and X-cause (or endogenous and exogenous) in the case of a community is given by the relation: i xy ii , in which, for each statistical unit„i”:
(xi, yi) represents numerical values of the variables X-cause and Y- effect; represents the point of intersection of the regression line with the Oy axis (constant term); represents the slope, (also called regression coefficient) and shows how many units Y and X change if you change the unit of measurement;
i is a residual variable (interpreted as error)
2,350
2,300
2,250
2,200 VI BI 2,150 Forecast(5)
2,100 BS
2,050
2,000
1,950 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
85 Journal "Annals – Economy Series", No. 16 / 2013
2,300
2,250
2,200 VI BI 2,150 SMA(5) BS 2,100
2,050
2,000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
From the previous grafics, we see that Forecast (5) aproximates better initial values (VI). Therefore define the following indicators: SMA )5( Forecast )5( MASF 2 Forecast )3( Forecast )5( MAF 2
2,260
2,240
2,220
2,200
2,180 VI 2,160 MASF
2,140 MAF
2,120
2,100
2,080
2,060 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
86 Journal "Annals – Economy Series", No. 16 / 2013
4,3800
4,3700
4,3600
4,3500
4,3400 VI Forecast(3) 4,3300 Forecast(5) 4,3200 SMA(5)
4,3100
4,3000
4,2900
4,2800 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
4,3600
4,3500
4,3400
VI 4,3300 MASF MAF
4,3200
4,3100
4,3000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
3. Conclusions From the above analyzed it is very difficult to say exactly the next value, knowing the past and the present. There are several ways to lead the lower and upper confidence interval
87 Journal "Annals – Economy Series", No. 16 / 2013 that will find the next value, but is impossible to determine exactly because uncertainty and many factors influence leaves its mark on this value. Previous graphs show that MAF has values closer to the the initial values than MASF, Forecast and SMA.
References: [1]. Mateia N. A., (2010) – Elemente de statistică economică şi econometrie, Editura Mirton, Timişoara; [2]. Ţiţan, E., Ghiţă, S., (2001) – Bazele statisticii, Aplicaţii, Editura Meteor Press, Bucureşti; [3]. Voineagu, V., Ţiţan, E., Şerban, R., Ghiţă, S., Todose, D., Boboc, C., Pele, D., (2007) – Teorie şi practică econometrică, Editura Meteor Press, Bucureşti; [4]. http://www.tranzactiiforex.ro; [5]. http://www.thewizardtrader.com.
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