Serii Cronologice

Se cunosc urmatoarele date privind numarul de posturi publice de radio si televiziune pe parcursul a 15 ani, incepand cu anul 1990:

MIJLOACELE DE RADIOCOMUNICATII (la sfarsitul anului)

Anii Statii publice de radio (y) Statii publice de televiziune (y’)

1990 100 41

1991 129 43

1992 129 47

1993 130 51

1994 131 51

1995 132 53

1996 125 58

1997 129 59

1998 134 62

1999 132 65

2000 140 74

2001 142 78

2002 144 83

2003 131 101

2004 163 113

Sursa: Institutul National de Statistica (www.insse.ro)

Datele statistice sunt preluate din “Transporturi, posta si telecomunicatii”

Se cere sa se calculeze sistemul de indicatori, sa se ajusteze seria folosind toate metodele cunoscute si sa se extrapoleze seria pentru anii 2007, 2008, 2009 si 2010.

Sa se reprezinte grafic evolutia numarului de statii publice de radio si televiziune, luand in considerare si anii 2007, 2008, 2009 si 2010.

Nr. Crt Anii (t)

y

y’ Modif.abs (pt.y) Modif.abs (pt.y’) Indici dinamica (pt.y) Indici dinamica (pt.y’) Ritmul dinamicii (pt.y) Ritmul dinamicii (pt.y’) Val.abs (pt.y) Val.abs (pt.y’)

fixa mobila fixa mobila fixa mobila fixa mobila fixa mobila fixa mobila fixa mobila fixa mobila

0 1990 100 41 0 - 0 - 1.000 - 1.000 - 0 - 0 - 1 - 0.41 -

1 1991 129 43 29 29 2 2 1.290 1.290 1.048 1.048 0.290 0.290 0.048 0.048 1 1.00 0.41 0.41

2 1992 129 47 29 0 6 4 1.290 1.000 1.146 1.093 0.290 0 0.146 0.093 1 1.29 0.41 0.43

3 1993 130 51 30 1 10 4 1.300 1.007 1.243 1.085 0.300 0.007 0.243 0.085 1 1.29 0.41 0.47

4 1994 131 51 31 1 10 0 1.310 1.007 1.243 1.000 0.310 0.007 0.243 0 1 1.30 0.41 0.51

5 1995 132 53 32 1 12 2 1.320 1.007 1.292 1.039 0.320 0.007 0.292 0.039 1 1.31 0.41 0.51

6 1996 125 58 25 -7 17 5 1.250 0.946 1.414 1.094 0.250 -0.054 0.414 0.094 1 1.32 0.41 0.53

7 1997 129 59 29 4 18 1 1.290 1.032 1.439 1.017 0.290 0.032 0.439 0.017 1 1.25 0.41 0.58

8 1998 134 62 34 5 21 3 1.340 1.038 1.512 1.050 0.340 0.038 0.512 0.050 1 1.29 0.41 0.59

9 1999 132 65 32 -2 24 3 1.320 0.985 1.585 1.048 0.320 -0.015 0.585 0.048 1 1.34 0.41 0.62

10 2000 140 74 40 8 33 9 1.400 1.060 1.804 1.138 0.400 0.060 0.804 0.138 1 1.32 0.41 0.65

11 2001 142 78 42 2 37 4 1.420 1.014 1.902 1.054 0.420 0.014 0.902 0.054 1 1.40 0.41 0.74

12 2002 144 83 44 2 42 5 1.440 1.014 2.024 1.064 0.440 0.014 1.024 0.064 1 1.42 0.41 0.78

13 2003 131 101 31 -13 60 18 1.310 0.909 2.463 1.216 0.310 -0.091 1.463 0.216 1 1.44 0.41 0.83

14 2004 163 113 63 32 72 12 1.630 1.244 2.756 1.118 0.630 0.244 1.756 0.118 1 1.31 0.41 1.01

TOTAL 1991 979 - 63 - 72 - 1.570 - 2.742 - - - - - - - -

Aceasta serie este o serie cronologica de flux deoarece inregistrarile se fac in anumite intervale de timp.

Sistemul de indicatori al seriilor cronologice

I. Indicatori absoluti

1) Nivelul caracteristicior individuale

{yi}, i=

Nivelul agregat al termenilor seriilor cronologice

∑yi=1991 ∑y’i=979

2) Modificarea absoluta

a) Pentru (y)

Cu baza fixa: Δn/0= yn-y0 Cu baza mobila: Δn/n-1= yn-yn-1

Δ0/0= y0-y0= 100-100= 0 Δ0/ -1= y0-y0-1= -

Δ1/0= y1-y0= 129-100= 29 Δ1/0= y1-y0= 129-100= 29

Δ2/0= y2-y0= 129-100= 29 Δ2/1= y2-y1= 129-129= 0

Δ3/0= y3-y0= 130-100= 30 Δ3/2= y3-y2= 130-129= 1

Δ4/0= y4-y0= 131-100= 31 Δ4/3= y4-y3= 131-130= 1

Δ5/0= y5-y0= 132-100= 32 Δ5/4= y5-y4= 132-131= 1

Δ6/0= y6-y0= 125-100= 25 Δ6/5= y6-y5= 125-132= -7

Δ7/0= y7-y0= 129-100= 29 Δ7/6= y7-y6= 129-125= 4

Δ8/0= y8-y0= 134-100= 34 Δ8/7= y8-y7= 134-129= 5

Δ9/0= y9-y0= 132-100= 32 Δ9/8= y9-y8= 132-134= -2

Δ10/0= y10-y0= 140-100= 40 Δ10/9= y10-y9= 140-132= 8

Δ11/0= y11-y0= 142-100= 42 Δ11/10= y11-y10= 142-140= 2

Δ12/0= y12-y0= 144-100= 44 Δ12/11= y12-y11= 144-142= 2

Δ13/0= y13-y0= 131-100= 31 Δ13/12= y13-y12= 131-144= -13

Δ14/0= y14-y0= 163-100= 63 Δ14/13= y14-y13= 163-131= 32

Relatia de verificare: ∑Δn/n-1=Δn/0 63=63 (Ad)