THE SEASONALITY OF TRANSACTIONS AND REAL ESTATE CYCLE  

The case of the city of Bordeaux

Benoit FAYE and Eric LE FURINSEEC Business Schools

June 27 2009

Litterature : a topic little explored

In France : Annual bulletin of INSEE presents the seasonal variations of prices according to the type of goods (apartment / house) and the type of region (Paris/ Province) (BEAUVOIS (2004, 2006))

In the USA : The sub-annual variations are presented either with the internal migrations (ROSEN (1979), WHEATON (1990), GOODMAN (1993), TUCKER, LONG and MARX (1995)) either with financial markets (KRAINER (2000), ORTALO-MAGNE and RADY (2005), ROSENTHAL (2006) )

In the research in real estate economy or in urban economy • Studies of long cycles analyze trends by neglecting generaly seasonality of the series

(FRIGGIT (2001a, 2003b), GRANELLE (1998), LAFERRÈRE and DUBUJET (2003)) • Studies of sub-annual cycles analyze seasonality by elimining trends in series

(FRIGGIT (2006), NGAI and TENREYRO (2008))

By consequence, it isn’t exist studies showing the link between the seasonality and the movements of market on the long term

Interests and risks of the negligence of the seasonality

0

500

1000

1500

2000

2500

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81

Seasonal movements are often considered as negligible

Series of medians of price per square meter

-15,000

-10,000

-5,000

0,000

5,000

10,000

15,000

20,000

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81

Quarterly growth rate of prices in Bordeaux on 85 quarters between

1985-1 and 2005-4

Quarterly growth rate of prices in the province (INSEE, 2004)

Using a nonlinear regression (polynomial) is common MED PM² = 321,045+30,076 t - 0,842 t² +8,409E-03 t3 (R²=0,986).

However, the heteroscedasticity resulting from a real seasonality makes doubtful the use of such a modeling approach .

We use a modeling of SARIMA by the method of BOX and JENKINS. This using permits us to identify an underlying model ARIMA (0, 2, 1) with a seasonal component (0, 2, 1). However, tests of normality of residue are doubtful and suggest the possibility of heteroscedasticity. In other words, the model could admit structural modifications, so under periods with differential fluctuations.

Statistic DDL Value p-value

Jarque-Bera 2 3,191 0,203

Box-Pierce 3 6,633 0,085

Ljung-Box 3 6,945 0,074

Box-Pierce 4 14,637 0,006

Ljung-Box 4 15,551 0,004

Stability tests on the residuals of the model

Research question and working assumptions

• This paper tries to identify the existence of links between the seasonality of transaction prices and the cycle of the residential market

• Two assumptions are successively posedH1: the residential market knows seasonality with characteristics which are disturbed by the cyclical movementsH2: disturbance of the seasonality doesn’t result of a modification of the transactions structure during the time.

Our database

• We use the database registered by the notarial network since 1985. This database notifies sales of residential goods (except social housing and new construction)

• This database presents two principal characteristics: representativeness : the number of registered transactions is very high representing a very strong cover rate.limited information: the number of considered variables by the database is weak in regard other databases available in France.

Characteristics of Bordeaux cycle

0,000

500,000

1000,000

1500,000

2000,000

2500,000

0 2000 4000 6000 8000 10000 12000 14000

number of transactions

Pm

²

first Quartile

Median third Quartile Mean

2005

1985

Our methodology

-1,000

-0,500

0,000

0,500

1,000

D2 D3 D4

Identification of phases of cycle

(Test of CHOW)

Choice of a reference period

(most little number of quarters presenting a stable

seasonality)

Calculation (from ti to ti+20) of the FAC for each sequence of 20 quarters(show of correlation coefficients for gaps of 1, 2, 3 and 4 quarters)

0

5

10

15

20

25

30

35

40

45

50

15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69

N = 20

ResultsGraphique 14 : Evolution trimestrielle des médianes

des pm²

0,000

500,000

1000,000

1500,000

2000,000

2500,000

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81

A1

A2

Breaking 1 Breaking 2

Phase 1 Phase 2 Phase 3

D4 medium amplitude

D4 weak amplitude

D4 high amplitude

Each type of surface presents a different seasonality

Gap 0-30 30-60 60-90 90-120 120-150 150-200 200-400 400+

4 0,252 0,194 0,219 0,246 0,340 0,271 0,280 0,230

8 0,027 0,257 0,229 0,239 0,282 0,242 0,224 0,126

During the 20 last years, the structure of the transactions by type of surface had changed with a strong growth of change of goods from 60 to 120 m².

It’s evident that the previous observations originate in part of a structure effect. This situation imposes the verification of the previous behaviors of

the series by type of surface.

Series of medians of price per square meter by striates of surface

500

1000

1500

2000

2500

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81

[0-30[ [30-60[ [60-90[ [90-120[

[120-150[ [150-200[ [200-400[ [400-max[

Observation of the link between rupture of trend and arrhythmia of seasonality

Link between rupture of the trend and time of arrhythmia during the first rupture

400- +

200-400

150-200

120-150

90-120

60-90

30-60 0-300,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

2 4 6 8 10 12 14 16

N1

a2/a

1

Link between rupture of the trend and time of arrhythmia during the second rupture

400-+

200-400

150-200

120-15090-120

60-90

30-600-30

0

5

10

15

20

25

30

6 8 10 12 14 16

N2

a3/a

2

By withdrawing the surface < 60 m² and > 400 m², the relationship between rupture of trend and arrhythmia length is linear.

Evaluation of the link between the arrhythmia and trend rupture

60-90

90-120

120-150

200-400

y = 0,0683x + 0,0181

R2 = 0,982

0,4

0,45

0,5

0,55

0,6

0,65

0,7

0,75

0,8

0,85

6 7 8 9 10 11 12 13

N1

60-90

90-120120-150

150-200

200-400

y = 0,4169x + 3,6726R2 = 0,1944

4

9

14

19

24

29

6 7 8 9 10 11 12 13 14 15 16

N2

a3/a

2

ConclusionsFinally, several interesting observations emerge from our study:

On the one hand, for the whole of transactions, two observations:Firstly, the amplitude of the seasonality declines with the growth rate of prices. Secondly, we have showed that the seasonality of the residential market of Bordeaux city was a real phenomenon but disturbed.

On the other hand, for the whole of transactions and more precisely for the surfaces situated between 60 and 120 m², two observations are important. Firstly, the amplitude of the seasonality is linked to the growth rate of the market. Secondly, each rupture of price trend implies an arrhythmia period with a length which is proportional to the importance of the rupture.

Any questions?