Workshop Matlab BITS Base

BITS: Serie Storiche in Matlab

Emmanuele Somma

Supporto Informatico per l’Area RicercheBanca d’Italia

21 Gennaio 2008

E. Somma (SIA-BdI) WMBB 2008 21/01/2008 1/96

Piano della presentazione

1 Le serie storiche in MATLABL’oggetto timeseriesL’oggetto fints

2 BITS - Bank of Italy Time SeriesL’oggetto tsmatCreazione della tsmatIndicizzazione per l’accessoRiorganizzazioneOperazioni tra le tsmatGestione dei MetadatiPlot

Le serie storiche in MATLAB

Serie storica Insieme di informazioni omogenee riferite a momenti diversiin successione temporale.

t2 v2...

...tn vn

Serie storica Insieme di osservazioni numeriche riferite a momenti diversiin successione temporale periodica.

t2p v2...

...tnp vn

L’oggetto timeseries

Un array dei dati

Un array di dati

x = [-0.2 -0.3 13;-0.1 -0.4 15;NaN 2.8 17;0.5 0.3 NaN;-0.3 -0.1 15]

Un array casuale di dati

x = rand(4,4);

Un paio di timeseries

ts_pos = timeseries(x(:,1:2), 1:5, ’name’, ’Position’)getdatasamplesize(ts_pos)

ts_vel = timeseries(x(:,3), 1:5, ’name’, ’Velocity’);getdatasamplesize(ts_vel)

Altre timeseries

%% Import the sample dataload count.dat

count1 = timeseries(count(:,1), 1:24,’name’, ’intersection1’);count2 = timeseries(count(:,2), 1:24,’name’, ’intersection2’);count3 = timeseries(count(:,3), 1:24,’name’, ’intersection3’);

get(count1)

Definizione delle unita di misuracount1.DataInfo.Units = ’cars’;count1.TimeInfo.Units = ’hours’;count2.TimeInfo.Units = ’hours’;count3.TimeInfo.Units = ’hours’;

Definizione del metodo d’interpolazione

count1.DataInfo.Interpolation = tsdata.interpolation(’zoh’);% zero-order hold

Aggiunta di eventi

%% Construct and add the first event to all time seriese1 = tsdata.event(’AMCommute’,8);

% Construct the first event at 8 AMe1.Units = ’hours’; % Specify the time units of the timecount1 = addevent(count1,e1); % Add the event to count1count2 = addevent(count2,e1); % Add the event to count2count3 = addevent(count3,e1); % Add the event to count3

Aggiunta di eventi

%% Construct and add the second event to all time seriese2 = tsdata.event(’PMCommute’,18);

% Construct the first event at 6 PMe2.Units = ’hours’; % Specify the time units of the timecount1 = addevent(count1,e2); % Add the event to count1count2 = addevent(count2,e2); % Add the event to count2count3 = addevent(count3,e2); % Add the event to count3

Collezioni di timeseries

tsc = tscollection({count1 count2},’name’, ’count_coll’)

tsc = addts(tsc, count3)

tsc1 = removets(tsc1,’intersection3’)

Ricampionamento della collezione

tsc1 = resample(tsc,1:2:24)tsc1 = resample(tsc,1:0.5:24)tsc1 = resample(tsc1,tsc1.Time)

Modifica dei contenuti degli elementi della collezione

tsc1 = addsampletocollection(tsc1,’time’,3.25,...’intersection1’,5)

tsc1 = delsamplefromcollection(tsc1,’index’,...find(isnan(tsc1.intersection2.Data)));

tsc1 = addsampletocollection(tsc1,’time’,3.25,...’intersection1’,5);

Modifica dei contenuti degli elementi della collezione

plot(tsc1.intersection1); hold on;plot(tsc1.intersection2)

L’oggetto fints

Creazione fints

dates = (datenum(’05/11/99’):datenum(’05/11/99’)+100)’;data_series1 = exp(randn(1, 101))’;data_series2 = exp(randn(1, 101))’;data = [data_series1 data_series2];myfts = fints(dates, data);myftsmyfts =desc: (none)freq: Unknown (0)’dates: (101)’ ’series1: (101)’ ’series2: (101)’’11-May-1999’ [ 0.6488] [ 0.1105]’12-May-1999’ [ 0.1891] [ 2.6814]’13-May-1999’ [ 1.1335] [ 0.5953][...]

Trasformazionesrs2 = myfts.series2

srs2_vec = fts2mat(myfts.series2)

format long g

srs2_mtx = fts2mat(myfts.series2, 1)

Indicizzazione elementiformat shortmyfts(’05/11/99’)myfts.series2(’05/11/99’)myfts.series2({’05/11/99’, ’05/21/99’, ’05/31/99’})myfts (’05/11/99::05/15/99’)myfts.series2(1)myfts.series2([1, 3, 5])myfts.series2(16:20)

Operazioniaddup = myfts1 + newftssubout = myfts1 - newftsaddscalar = myfts1 + 10000submtx = myfts1 - randn(20, 4)

Operazioni

newfts2 = fints(myfts1.dates, fts2mat(myfts1/10000),...{’Rat1’,’Rat2’, ’Rat3’,’Rat4’}, 1, ’New FTS’)

addother = myfts1 + fts2mat(newfts2);

BITS - Bank of Italy Time Series

L’oggetto tsmat

Costruzione tsmat

TSMAT = tsmat(1980,1,12,count)tsmat( macro index (year), micro index (period), frequency, data matrix )

Parametri

macro index double (used as integer)micro index double (used as integer)frequency numero di elementi in una divisione macro

1 Year2 Semester4 Quarter12 Month52 Week365 Day

data matrix NOBS!NSERIESSERIES colonneOSSERV righe

Esempio

A = tsmat(1980,1,12,rand(20,1))Tsmat object

Size: [20 1]Frequency: 12

Start: 1980 1End: 1981 8

Labels: T1

B = tsmat(1980,1,12,rand(20,1))

BG = tsmat(1980,1,365,rand(220,1))Tsmat object

Start: Tue Jan-01-1980End: Thu Aug-07-1980

Labels: T1

Caricamento datiload count.datTSC = tsmat(1980,1,365,count)Tsmat object

Start: Tue Jan-01-1980End: Thu Jan-24-1980

Labels: T1 T2 T3

Strutturastruct(TSC)ans =

matdata: [24x3 double]start_year: 1980

start_period: 1freq: 365

last_year: 1980last_period: 24

meta: [1x1 struct]meta_cols: [1x1 struct]

I ValoriTSC.matdataans =

11 11 97 13 1114 17 2011 13 943 51 6938 46 7661 132 186[...]

I metadati di base

.freq frequenza delle osservazioni

.start indice dell’oss. iniziale (anno,periodo)

.start year anno dell’oss. iniziale

.start period periodo dell’oss. iniziale

.last indice dell’oss. finale (calcolato)

.last year anno dell’oss. finale (calcolato)

.last period periodo dell’oss. finale (calcolato)

.range vettore degli indici iniziale e finale

.dates vettore delle date in formato num. Matlab

.matdata matrice dei valori della collezione

Ad es.datestr(TSC.dates)ans =01-Jan-198002-Jan-198003-Jan-1980[...]

I metadati ’estesi’

.meta metadati della collezione

.meta cols metadati delle colonne

I metadati di colonna obbligatori

’label’ nome della serie

Ad es.TSC.metaans =

release: 733425TSC.meta_colsans =

label: {’T1’ ’T2’ ’T3’}

Visualizzare una serie con tstab

tstab(S1 [, S2 ...]) dove S1,...,S2 sono oggetti tsmatA=tsmat(1980,1,12,rand(5,1))B=tsmat(1980,3,12,rand(5,1))tstab(A,B)tsStart: 1980 1tsRelease: 18-Jan-2008Frequency: 12 (monthly)Date

T1 T118/01/08 18/01/08

1980-M-001 0.0377 NaN1980-M-002 0.8852 NaN1980-M-003 0.9133 0.26191980-M-004 0.7962 0.33541980-M-005 0.0987 0.67971980-M-006 NaN 0.13661980-M-007 NaN 0.7212

Creazione della tsmat

tsmat: Come si usa>>

ts = tsmat(1980,1,12,rand(3,4))Tsmat object

Size: [3 4]Start: 1980 1End: 1980 3

Labels: T1 T2 T3 T4>> get(ts)

tsmat: Come si usa>> ts = tsmat(1980,1,12,rand(3,4))

Tsmat objectSize: [3 4]Start: 1980 1End: 1980 3

tsmat: Come si usa>> ts = tsmat(1980,1,12,rand(3,4))Tsmat object

Size: [3 4]Start: 1980 1End: 1980 3

Labels: T1 T2 T3 T4>>

get(ts)matdata: [3x4 double]

start_year: 1980start_period: 1

freq: 12last_year: 1980

last_period: 3meta: [1x1 struct]

meta_cols: [1x1 struct]

Size: [3 4]Start: 1980 1End: 1980 3

tsmat: Come si usa>>

tstab(ts)tsStart: 1980 1tsRelease: 17-Jul-2007

RELEASES

Frequency: 12 (monthly)Date

LABELS