TIME SERIES AND REGRESSION APPLIED TO HOUSING PRICE
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1 TIME SERIES AND REGRESSION APPLIED TO HOUSING PRICE
2 CONTENT DESCRIPTIVE ANALYSIS OF THE HOUSING PRICE EVOLUTION AND THE MIBOR BY MEANS OF TIME SERIES CONCLUSIONS ON RELATIONSHIP AMONG AVERAGE PRICE OF THE M 2, ICP AND THE MIBOR REGRESSION ANALYSIS
3 TIME SERIES A time series, is a sequece of observatios, (t,y t ) which are ordered i time. APPLICATION: a) The series of average price of square meter i Spai from 1987 to b) The series of the referece idex MIBOR from 1987 to 2003.
4 TIME SERIES COMPONENTS 1. Tred (T); it reflects its evolutio i the log term. 2. Seasoal compoet (S), it gathers the oscillatios of repetitio i periods of time equal or less tha oe year. 3. Cyclical compoet (C), it gathers periodic oscillatios of amplitude higher tha oe year. 4. Irregular compoet (I), it gathers the erratic fluctuatios due to uforeseeable pheomea, kow also like residual or erratic compoet.
5 MODELS USED FOR THE STUDY OF TIME SERIES I the classic study of time series, oe deals with two hypothesis of work: The multiplicative hypothesis : Y(t)=T*C*S*I The additive hypothesis : Y(t)=T+C+S+I A aalytical form to determie which model fits best is the method of seasoal quotiets ad differeces.
6 The method of seasoal quotiets ad differeces We calculate the series of the differeces (d) ad the quotiets oe (q) betwee two cosecutive seasos from differet years; CV(d)= Stadard deviatio(d) Average(d) CV(q)= Stadard deviatio(q) Average(q) If CV( q) CV ( d) the we use the multiplicative model If CV( q) > CV( d) the we use the additive model
7 Quarterly data of the average price of m 2 Year Price of m 2 Year Price of m2 Year Price of m2 Year Price of m2 Year Price of m T T T T T 1, T T T T T 1, T T T T T 1, T T T T T T T T T T T T T T T T T T T T T T T T T T T T 1, T T T T 1, T T T T 1, T T T T 1, T T T T 1, T T T T 1, T T T T 1, Data provided by the Spaish Miistry, Miisterio de Fometo This time series follows a multiplicative model
8 Represetatio of the compoets series Euros/m , , , ,00 800,00 600,00 400,00 200,00 0,00 Time series Tred Cyclical compoet Irregular Compoet Seasoal compoet T 4T 3T 2T T 4T 3T 2T T 4T 3T Year 2T T 4T 3T 2T T 4T 3T 2T T 4T 3T
9 Represetatio of the compoets series MIBOR TIME SERIES
10 ICP, MIBOR AND AVERAGE PRICE OF m Euro/m Average price m2 MIBOR ICP quarters Yearly variatio of m 2 price, ICP, MIBOR 200,00 Variatios(%) 150,00 100,00 50,00 0,00 Yearly variatio m2 Yearly variatio ICP Yearly variatio Mibor -50, Year
11 CONCLUSIONS The behaviour of housig price, is a very complex ecoomic cocept to be modelled by meas of time series. May other factors ifluece housig price evolutio, amog them, the ICP ad the referece idex of mortgage rates. Therefore i the last years the low iterest rates have created a high housig demad ad hece a high iflatio. It would be iterestig to study these cocepts together usig regressio aalysis.
12 Simple liear regressio How ca we get a fuctioal relatioship betwee two variables? I our case, we try to explai the MIBOR through the time, this meas, the MIBOR is the depedet variable ad the time the idepedet oe. I this way we ca predict the MIBOR idex for the ext year. We use the least squares method.
13 Method of least squares A least-squares approximatio is fittig a lie to a set of paired (x i,y i ) observatios. The lie is; y( x) = a + bx + e The goal is to miimize the error, the discrepacy betwee the true value y ad the approximate value a + bx 2 2 e 1 i = y 1 i, measured yi,model = yi b axi 1 mi mi ( ) mi ( )
14 Method of the least squares To obtai these coefficiets, we differetiate this expressio with respect to these coefficiets ad we obtai, b = x y x y a = y b x x x 1 i i 1 i 1 i 2 2 ( ) 1 i 1 i To simplify this calculatios, we do a chage of variable i x to make x ' = 0 order to get 1 2 x ' i y i b = a = y x ' i 1 i
15 Coefficiet of determiatio With this chage of variable i x we get a very simple expressio for the coefficiet of determiatio, it shows how good is the regressio 2 ( S 2 x '. y ) R = 2 2 S S x ' y 1 S = x ' ' t' y 1 i yi x y 1 1 S x x S y y t' = ( ') ( ') ( ) 1 i y = 1 i
16 Calculatios to get the regressio lie by meas of least squares method
17 Results of the regressio a b 1 i = = = 2 1 y 2 i ' yx 1 i i = = = 0.87 x ' 408 x ' = ( x 1995) y( x) = a + bx ' = a + b( x 1995) = 0.87x R = 0.89% The predictio for 2004 is; y(2004) = 0.872x = 0.87
18 Simple liear regressio Year Regressio MIBOR MIBOR
S Y Y = ΣY 2 n. Using the above expressions, the correlation coefficient is. r = SXX S Y Y
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