>h SSKJrJrJrJr SSKJrJr SSKr SSK J r J r SSK JrJr SSKrSSKrSSKJr SSKJr SSKJrJrJrJr SS KJr \ \ R\R>\R@4r!\ \"\RF4r$S r%"S S \5r&"S S\&\5r'"SS\'5r("SS\&5r)"SS\&\5r*"SS\*5r+"SS\&\5r,"SS\,\*5r-"SS\,5r."SS\,\'5r/"SS 5r0g)!) PD_LT_2_2_0Appender is_int_indexto_numpy)ABCabstractmethodN)OptionalUnion)HashableSequence)qr)d_or_f) bool_like float_likerequired_int_like string_like)freq_to_periodzstart is less than the first observation in the index. Values can only be created for observations after the start of the index. c \rSrSrSrSr\S\4Sj5r\ S\ \ S\ R4Sj5r\ SS \S\ \ S \\ \ S\ R4S jj5r\ S\4S j5rS\4S jr\\ S\\ S44Sj55r\S\ \ S\ R04Sj5r\SS\ R0S \S \\ \ S\ R04Sjj5rS\4SjrS\S\4SjrSrg)DeterministicTerm$z/Abstract Base Class for all Deterministic TermsFreturncUR$)z?Flag indicating whether the values produced are dummy variables) _is_dummyselfs pC:\Users\julio\OneDrive\Documentos\Trabajo\Ideas Frescas\venv\Lib\site-packages\statsmodels/tsa/deterministic.pyis_dummyDeterministicTerm.is_dummy*~~indexcg)z Produce deterministic trends for in-sample fitting. Parameters ---------- index : index_like An index-like object. If not an index, it is converted to an index. Returns ------- DataFrame A DataFrame containing the deterministic terms. Nrr!s r in_sampleDeterministicTerm.in_sample/r Nstepsforecast_indexcg)a Produce deterministic trends for out-of-sample forecasts Parameters ---------- steps : int The number of steps to forecast index : index_like An index-like object. If not an index, it is converted to an index. forecast_index : index_like An Index or index-like object to use for the forecasts. If provided must have steps elements. Returns ------- DataFrame A DataFrame containing the deterministic terms. Nr#)rr(r!r)s r out_of_sampleDeterministicTerm.out_of_sample@r'r cg)z.A meaningful string representation of the termNr#rs r__str__DeterministicTerm.__str__[r'r c\[U5R4n[XR-5$N)type__name__hash_eq_attr)rnames r__hash__DeterministicTerm.__hash___s&&*4j&9&9%;D==())r .cg)z9tuple of attributes that are used for equality comparisonNr#rs rr5DeterministicTerm._eq_attrcr'r c[U[R5(aU$[R"U5$![a [ S5ef=f)Nz*index must be a pandas Index or index-like) isinstancepdIndex Exception TypeErrorr!s r _index_likeDeterministicTerm._index_likehsI eRXX & &L J88E? " JHI I Js 9Ac$Ubj[RU5n[U[R5(deUR SU:wa[ SUR SSUS35eU$[U[R5(a%[R"USS-XRS9$[U[R5(aRURbE[R"USURS S 9Sn[R"X0RUS 9$[U[R5(aV[U[R5(deURnURnXTU--n[R"XVUS 9$[#U5(an[$R&"[$R("U5S:H5(a<[$R*"USS-USU-S-5n[R"U5$SSKnUR/S [0S S9 UR Sn [R"U S-X-S-5$![a( [!U5S:a USUS - OSnUSU-nGNf=f)zExtend the forecast indexNrz(The number of values in forecast_index (z) must match steps (z).periodsfreqrIrHstepzOnly PeriodIndexes, DatetimeIndexes with a frequency set, RangesIndexes, and Index with a unit increment support extending. The index is set will contain the position relative to the data length.) stacklevel)rrBr<r=r>shape ValueError PeriodIndex period_rangerI DatetimeIndex date_range RangeIndexrNstopAttributeErrorlenrnpalldiffarangewarningswarn UserWarning) r!r(r)next_obsrNstartrWidx_arrr^nobss r _extend_indexDeterministicTerm._extend_indexqsE  %.::>JNnbhh77 77##A&%/ &,,Q/00DUG2O" ! eR^^ , ,??b A u:: r// 0 0UZZ5K}}U2YUZZKANH== EJ J r}} - -eR]]33 33 )zz  %<'D==48 8 % RVVBGGENa,?%@%@iib A uRy5/@1/DEG88G$ $  "   {{1~}}TAXt|a'788+" )03E QuRy59,Ab D( )s$I.JJcBUR5S[U5S3-$)Nz at 0x0x)r.idrs r__repr__DeterministicTerm.__repr__s ||~&D" 666r otherc[U[U55(a\URnURn[U5[U5:wag[ [ X#5VVs/sH upEXE:HPM snn5$gs snnf)NF)r<r2r5rYr[zip)rrlown_attroth_attrabs r__eq__DeterministicTerm.__eq__sf eT$Z ( (}}H~~H8}H -3x+BC+B41+BCD DDsA8 r#r1)r3 __module__ __qualname____firstlineno____doc__rpropertyboolrrr r r= DataFramer%intr r+strr.r7tupler5 staticmethodr>rBrerjobjectrs__static_attributes__r#r rrr$s9I $ x1 bll   8<   ! !(!34     4===*#*H%# .HHJ8H-J"((JJ8<09xx0909!(!3409  0909d7#7Ftr rc\rSrSrSrSS\S\SS4Sjjr\S\4Sj5r \S\4S j5r \S\ \ 4S j5r S \RS\R4S jrS\ 4S jrSrg)TimeTrendDeterministicTermz:Abstract Base Class for all Time Trend Deterministic TermsconstantorderrNcH[US5Ul[US5Ulg)Nrr)r _constantr_order)rrrs r__init__#TimeTrendDeterministicTerm.__init__s"8Z8'w7 r cUR$)z+Flag indicating that a constant is included)rrs rr#TimeTrendDeterministicTerm.constantrr cUR$)zOrder of the time trendrrs rr TimeTrendDeterministicTerm.order{{r c/nSSSS.nUR(aURS5 [SURS-5H1nX2;aURX#5 MURSU35 M3 U$)Ntrend trend_squared trend_cubed)rFrJconstrFztrend**)rappendranger)rcolumns trend_namespowers r_columns#TimeTrendDeterministicTerm._columnssn!o-H >> NN7 #1dkkAo.E#{1201 / r locsc6[UR5UR-n[R"USU45n[R "SU4[S9n[R "SURS-5US[UR5S24'X4-nU$)NrFdtyper)r|rrrZtilezerosr])rrntermstermsrs r _get_terms%TimeTrendDeterministicTerm._get_termss{T^^$t{{2q&k*!VC0*,))At{{Q*GaT^^$&&'  r c/nUR(aURS5 UR(a!URSURS-35 U(dS/nSRU5nSUS3$)NConstantz Powers 1 to rFEmpty,z TimeTrend())rrrjoin)rr terms_strs rr."TimeTrendDeterministicTerm.__str__sc >> LL $ ;; LL< a'89 :IEHHUO I;a((r rrTr)r3rurvrwrxrzr|rryrrlistr}rrZndarrayrr.rr#r rrrsD88S88$s $s)  rzzbjj ) )r rc ^\rSrSrSrSS\S\SS4U4Sjjjr\S\ SS4S j5r \ "\ RR5S \\\\R$4S\R&4S j5r \ "\ R(R5SS \S \\\\R$4S \\\S\R&4Sjj5r\S\\S44Sj5rSrU=r$) TimeTrenda Constant and time trend determinstic terms Parameters ---------- constant : bool Flag indicating whether a constant should be included. order : int A non-negative int containing the powers to include (1, 2, ..., order). See Also -------- DeterministicProcess Seasonality Fourier CalendarTimeTrend Examples -------- >>> from statsmodels.datasets import sunspots >>> from statsmodels.tsa.deterministic import TimeTrend >>> data = sunspots.load_pandas().data >>> trend_gen = TimeTrend(True, 3) >>> trend_gen.in_sample(data.index) rrrNc$>[TU]X5 gr1)superr)rrr __class__s rrTimeTrend.__init__s )r rcVURS5nSnSU;aSnOSU;aSnU"X#S9$)a Create a TimeTrend from a string description. Provided for compatibility with common string names. Parameters ---------- trend : {"n", "c", "t", "ct", "ctt"} The string representation of the time trend. The terms are: * "n": No trend terms * "c": A constant only * "t": Linear time trend only * "ct": A constant and a time trend * "ctt": A constant, a time trend and a quadratic time trend Returns ------- TimeTrend The TimeTrend instance. crttrJtrFrr startswith)clsrrrs r from_stringTimeTrend.from_strings<.##C( 5=E E\EH22r r!cURU5nURSn[R"SUS-[RS9SS2S4nUR U5n[ R"X@RUS9$NrrFrrr!) rBrPrZr]doublerr=r{r)rr!rdrrs rr%TimeTrend.in_sample!sg  '{{1~yyD1HBII6q$w?%||E==FFr r(r)c,URU5nURSnURX!U5n[R"US-XA-S-[R S9SS2S4nUR U5n[R"XpRUS9$r) rBrPrerZr]rrr=r{r)rr(r!r)rd fcast_indexrrs rr+TimeTrend.out_of_sample+s  '{{1~((~F yy4r{r+r ryr~r5r __classcell__rs@rrrs64**S***33 33<))112G8H-rxx78G G3G--556 8< M MXh'12 M!(!34 M  M7 M+%# .++r rc 4\rSrSrSrSrSS\S\SS4Sjjr\S\4S j5r \S\4S j5r \ S \ \ \\R \R"4SS4S j5r\S\\S 44Sj5rS\4Sjr\S\\4Sj5r\"\R6R5S \ \ \\R84S\R:4Sj5r\"\R<R5SS\S \ \ \\R84S\\ \S\R:4Sjj5rSr g) Seasonalityi>a Seasonal dummy deterministic terms Parameters ---------- period : int The length of a full cycle. Must be >= 2. initial_period : int The seasonal index of the first observation. 1-indexed so must be in {1, 2, ..., period}. See Also -------- DeterministicProcess TimeTrend Fourier CalendarSeasonality Examples -------- Solar data has an 11-year cycle >>> from statsmodels.datasets import sunspots >>> from statsmodels.tsa.deterministic import Seasonality >>> data = sunspots.load_pandas().data >>> seas_gen = Seasonality(11) >>> seas_gen.in_sample(data.index) To start at a season other than 1 >>> seas_gen = Seasonality(11, initial_period=4) >>> seas_gen.in_sample(data.index) Tperiodinitial_periodrNc[US5Ul[US5UlUS:a [S5eSURs=::aU::d O [S5eg)NrrrJzperiod must be >= 2rFz-initial_period must be in {1, 2, ..., period})r_period_initial_periodrQ)rrrs rrSeasonality.__init__cs\(: 0 ,  A:23 3D((2F2LM M3r cUR$)zThe period of the seasonalityrrs rrSeasonality.periodm||r cUR$)z+The seasonal index of the first observation)rrs rrSeasonality.initial_periodrs###r r!cbURU5n[U[R5(a URnOT[U[R 5(a*UR(a URO UR nO [S5eUc [S5e[U5nU"US9$)z Construct a seasonality directly from an index using its frequency. Parameters ---------- index : {DatetimeIndex, PeriodIndex} An index with its frequency (`freq`) set. Returns ------- Seasonality The initialized Seasonality instance. z,index must be a DatetimeIndex or PeriodIndexz+index must have a freq or inferred_freq set)r) rBr<r=rRrIrT inferred_freqr@rQr)rr!rIrs r from_indexSeasonality.from_indexws"& eR^^ , ,::D r// 0 0!&5::1D1DDJK K <JK K%&!!r .c2URUR4$r1)rrrs rr5Seasonality._eq_attrs||T1111r c"SURS3$)NzSeasonality(period=rrrs rr.Seasonality.__str__s$T\\N!44r c~URn/n[SUS-5HnURSUSUS35 M U$)NrFs(rr)rrr)rrris rrSeasonality._columnssEq&1*%A NNRs!F81- .&r c(URU5nURSnURn[R"X#45nUR S- n[ U5HnXe-U-nSXFSU2U4'M [R"X@RUS9$NrrFr) rBrPrrZrrrr=r{r)rr!rdrtermoffsetrcols rr%Seasonality.in_samples  '{{1~xx'%%)vA:'C#$DFC ||D--uEEr r(r)cRURU5nURX!U5nURSnURn[R "X45nUR S- n[U5Hn XX-U -U-n SXySU2U 4'M [R"XpRUS9$r) rBrerPrrZrrrr=r{r) rr(r!r)rrdrrrrcol_locs rr+Seasonality.out_of_samples  '((~F {{1~xx(%%)vA}q(F2G'(DFG# $||D--{KKr )rr)rFr1)!r3rurvrwrxrr|rryrrrr r r r=rTrRrr~r5r}r.rrrrr%r>r{r+r rr#r rrr>s DINsNCNN$$$"(8,b.>.>NO" ""82%# .2255$s)))112 F8H-rxx78 F  F3 F--556 8< LLXh'12L!(!34 L  L7Lr rc|\rSrSrSrS\SS4Sjr\S\4Sj5rS\ RS\ R4S jr S r g) FourierDeterministicTermiz7Abstract Base Class for all Fourier Deterministic TermsrrNc&[US5UlgNr)rr)rrs rr!FourierDeterministicTerm.__init__s'w7 r cUR$)z'The order of the Fourier terms includedrrs rrFourierDeterministicTerm.orderrr rcS[R-UR[R5-n[R"UR SSUR -45n[UR 5HPn[[R[R45H upEU"US-U-5USS2SU-U-4'M" MR U$)NrJrrF) rZpiastyperemptyrPrr enumeratesincos)rrrrjfuncs rr#FourierDeterministicTerm._get_termss255y4;;ryy11$**Q-T[[9:t{{#A$bffbff%56&*AET>&:aQl#7$ r r) r3rurvrwrxr|rryrrZrrrr#r rrrsNA8c8d8srzzbjjr rc ^\rSrSrSrSrS\S\4U4Sjjr\ S\4Sj5r \ S\ \ 4S j5r \"\R R5S \\\\R*4S\R,4S j5r\"\R.R5SS \S \\\\R*4S \\\S\R,4Sjj5r\ S\\S44Sj5rS\ 4SjrSrU=r$)Fourieria% Fourier series deterministic terms Parameters ---------- period : int The length of a full cycle. Must be >= 2. order : int The number of Fourier components to include. Must be <= 2*period. See Also -------- DeterministicProcess TimeTrend Seasonality CalendarFourier Notes ----- Both a sine and a cosine term are included for each i=1, ..., order .. math:: f_{i,s,t} & = \sin\left(2 \pi i \times \frac{t}{m} \right) \\ f_{i,c,t} & = \cos\left(2 \pi i \times \frac{t}{m} \right) where m is the length of the period. Examples -------- Solar data has an 11-year cycle >>> from statsmodels.datasets import sunspots >>> from statsmodels.tsa.deterministic import Fourier >>> data = sunspots.load_pandas().data >>> fourier_gen = Fourier(11, order=2) >>> fourier_gen.in_sample(data.index) Frrc>[TU]U5 [US5UlSUR-UR:a [ S5eg)NrrJz2 * order must be <= period)rrrrrrQ)rrrrs rrFourier.__init__sC !&(3 t{{?T\\ ):; ; *r rcUR$)zThe period of the Fourier termsrrs rrFourier.periodrr c URn[U5R5n/n[SURS-5H&nSHnUR USUSUS35 M M( U$)NrFrr(rr)rrstriprrr)rr fmt_periodrrtyps rrFourier._columns skF^))+ q$++/*A%#as!J?||E FFr r(r)cURU5nURX!U5nURSnUR[R "XUU-5UR - 5n[R"XdURS9$r) rBrerPrrZr]rr=r{r)rr(r!r)rrdrs rr+Fourier.out_of_samplesl  '((~F {{1~ $u = LM||EdmmLLr .c2URUR4$r1rrrs rr5Fourier._eq_attr,s||T[[((r c<SURSURS3$)NzFourier(period=, order=rrrs rr.Fourier.__str__0s ht{{m1EEr rr1)r3rurvrwrxrfloatr|rryrrr}rrrr%r r r r=r>r{r+r r~r5r.rrrs@rrrs^%LIzz!!!r r!cb[U[R5(aUR5nXR UR 5R5- nUR UR 5nUS-R5UR5- n[ U5[ U5- $)NrF)r<r=rR to_timestamp to_periodr$r)rr!deltargaps r_compute_ratio(CalendarDeterministicTerm._compute_ratioCs eR^^ , ,&&(E 3@@BB __TZZ (Av##%(99#..r allowed.c[U[5(aU4n[X5(d[U5S:XaSUSR-nODSR SUSS55n[U5S:aUS- nUS USR-- n[U5RS U3n[ U5e[U[ R[ R45(deU$) NrFza rz, c38# UHoRv M g7fr1)r3).0rqs r >CalendarDeterministicTerm._check_index_type..[s)Kl**lsrErJrz and z! terms can only be computed from ) r<r2rYr3rr@r=rTrR)rr!r3 allowed_typesmsgs r_check_index_type+CalendarDeterministicTerm._check_index_typeMs gt $ $jG%))7|q $wqz':': : $ )Kgcrl)K K wr2r~r;rr#r rr"r"4s>ASATA"c""/2++R^^;</ /    NN2 xxtU49--. r/ 0r r"c ^\rSrSrSrS\S\SS4U4Sjjr\S\ \4Sj5r \ "\ RR5S \\\\R$4S\R&4S j5r \ "\ R(R5SS \S \\\\R$4S \\\S\R&4S jj5r\S\\S44Sj5rS\4SjrSrU=r$)CalendarFourieriha Fourier series deterministic terms based on calendar time Parameters ---------- freq : str A string convertible to a pandas frequency. order : int The number of Fourier components to include. Must be <= 2*period. See Also -------- DeterministicProcess CalendarTimeTrend CalendarSeasonality Fourier Notes ----- Both a sine and a cosine term are included for each i=1, ..., order .. math:: f_{i,s,t} & = \sin\left(2 \pi i \tau_t \right) \\ f_{i,c,t} & = \cos\left(2 \pi i \tau_t \right) where m is the length of the period and :math:`\tau_t` is the frequency normalized time. For example, when freq is "D" then an observation with a timestamp of 12:00:00 would have :math:`\tau_t=0.5`. Examples -------- Here we simulate irregularly spaced hourly data and construct the calendar Fourier terms for the data. >>> import numpy as np >>> import pandas as pd >>> base = pd.Timestamp("2020-1-1") >>> gen = np.random.default_rng() >>> gaps = np.cumsum(gen.integers(0, 1800, size=1000)) >>> times = [base + pd.Timedelta(gap, unit="s") for gap in gaps] >>> index = pd.DatetimeIndex(pd.to_datetime(times)) >>> from statsmodels.tsa.deterministic import CalendarFourier >>> cal_fourier_gen = CalendarFourier("D", 2) >>> cal_fourier_gen.in_sample(index) rIrrNcp>[TU]U5 [RX5 [US5Ulgr)rrrrr)rrIrrs rrCalendarFourier.__init__s,  ))$6'w7 r c /n[SURS-5H:nSH1nURUSUSURRS35 M3 M< U$)NrFrrz,freq=r)rrrr$r))rrrrs rrCalendarFourier._columnss[q$++/*A%#as&1C1C0DAFG&+r r!cURU5nURU5nURU5nURU5n[R "X1UR S9$Nr)rBr;r1rr=r{r)rr!ratiors rr%CalendarFourier.in_samplesW  '&&u-##E*&||E FFr r(r)cNURU5nURX!U5nURU5 [U[R [R 45(deURU5nURU5n[R"XdURS9$rD) rBrer;r<r=rTrRr1rr{r)rr(r!r)rrErs rr+CalendarFourier.out_of_samples  '((~F  {++(8(8"..'IJJJJ##K0&||EdmmLLr .cFURRUR4$r1r$r)rrs rr5CalendarFourier._eq_attrszz!!4;;..r cPSURRSURS3$)Nz Fourier(freq=rrrJrs rr.CalendarFourier.__str__s&tzz112(4;;-qIIr rr1)r3rurvrwrxr}r|rryrrrrr%r r r r=r>r{r+r r~r5r.rrrs@rr>r>hsC.`8S888 $s)))112G8H-rxx78G G3G--556 8< M MXh'12 M!(!34 M  M7 M/%# .//JJJr r>c $^\rSrSrSrSr\(aSSSSS.SSS .S S S .S S S .S S S S.S.rO SSSS.SS0S S S.S S S S.S S S S.SS 0S S S.S.rS\S\SS4U4Sjjr \ S\4Sj5r \ S\4Sj5r S\ \R\R 4S\R$4SjrS\ \R\R 4S\R$4S jrS\ \R\R 4S\R$4S!jrS\ \R\R 4S\R$4S"jrS\ \R\R 4S\R$4S#jr\ S\\4S$j5r\"\R8R5S\ \\\R>4S\R@4S%j5r\"\RBR5S-S&\"S\ \\\R>4S'\#\\S\R@4S(jj5r!\ S\$\S)44S*j5r%S\4S+jr&S,r'U=r($).CalendarSeasonalityiaN Seasonal dummy deterministic terms based on calendar time Parameters ---------- freq : str The frequency of the seasonal effect. period : str The pandas frequency string describing the full period. See Also -------- DeterministicProcess CalendarTimeTrend CalendarFourier Seasonality Examples -------- Here we simulate irregularly spaced data (in time) and hourly seasonal dummies for the data. >>> import numpy as np >>> import pandas as pd >>> base = pd.Timestamp("2020-1-1") >>> gen = np.random.default_rng() >>> gaps = np.cumsum(gen.integers(0, 1800, size=1000)) >>> times = [base + pd.Timedelta(gap, unit="s") for gap in gaps] >>> index = pd.DatetimeIndex(pd.to_datetime(times)) >>> from statsmodels.tsa.deterministic import CalendarSeasonality >>> cal_seas_gen = CalendarSeasonality("H", "D") >>> cal_seas_gen.in_sample(index) T)BDhHrUrVr)MSM )rYQrZ)WrTr]AY)rSrTrUrU)rYME)rYraQEra)rarb)r^rTr]r_r`rbYErIrrNc >[5nUR"URR5Vs/sHn[ UR 55PM sn6 [ URR 55n[US[ U5SS9n[USUSS9nXRU;a[SUSUS35e[TU])U5 X l URRRS5S Ulgs snf) NrIF)optionslowerrzThe combination of freq=z and period=z is not supported.-r)setupdate _supportedvaluesrkeysr~rrQrrrr$r)split _freq_str)rrIr freq_optionsvalperiod_optionsrs rrCalendarSeasonality.__init__s!$ *.//*@*@*B C*B3d388:*B C t3356 &% "5U  HnE  v. .*4&1 !35   ++11#6q9#Ds#Dc.URR$r'r(rs rrICalendarSeasonality.freqr+r cUR$)zThe full periodrrs rrCalendarSeasonality.periodrr r!cURRS;aURSUR--$URRS:Xa UR$[R "SSS9RR 5nURnURU5R5(d [S5eU$)NrXrWrTz2000-1-1 )rHz=freq is B but index contains days that are not business days.) r$r)hour dayofweekr= bdate_rangeuniqueisinr[rQ)rr!bdayslocs r_weekly_to_loc"CalendarSeasonality._weekly_to_loc"s ::   +::U__ 44 4 ZZ  3 &?? "NN:r:DDKKME//C88E?&&(( Jr cUR$r1)ryr$s r _daily_to_loc!CalendarSeasonality._daily_to_loc3szzr c&URS- S-$)NrFr)monthr$s r_quarterly_to_loc%CalendarSeasonality._quarterly_to_loc8s a1$$r crURRS;aURS- $URS- $)N)rZrarYrF)r$r)rquarterr$s r_annual_to_loc"CalendarSeasonality._annual_to_loc=s4 ::  !2 2;;? "==1$ $r cURS:XaURU5nOUURS:XaURU5nO3URS;aURU5nOUR U5nUR URUR n[R"URSU45nSU[R"URS5U4'U$)NrTr^)r]rbrrF) rrrrrrjrnrZrrPr])rr!r full_cyclers rrCalendarSeasonality._get_termsEs <<3 %%e,D \\S &&u-D \\[ ())%0D&&u-D__T\\24>>B $**Q-4501bii 1 &,- r c /nURURURn[U5H5nUR SURSUS-SURS35 M7 U$)Nr=rFz , period=r)rjrrnrr)rrcountrs rrCalendarSeasonality._columnsUsh -dnn=uA NNT^^$Aa!eWIdll^1E r cURU5nURU5nURU5n[R"X!UR S9$rD)rBr;rr=r{r)rr!rs rr%CalendarSeasonality.in_sample_sG  '&&u-&||E FFr r(r)c,URU5nURX!U5nURU5 [U[R [R 45(deURU5n[R"XTURS9$rD) rBrer;r<r=rTrRrr{r)rr(r!r)rrs rr+!CalendarSeasonality.out_of_sampleisy  '((~F  {++(8(8"..'IJJJJ ,||EdmmLLr .c2URUR4$r1)rrnrs rr5CalendarSeasonality._eq_attrws||T^^++r c"SURS3$)NzSeasonal(freq=r)rnrs rr.CalendarSeasonality.__str__{s/q11r )rnrr1))r3rurvrwrxrrrjr}rryrIrr r=rTrRrZrrrrrrrrrrr%r r r>r{r+r|r r~r5r.rrrs@rrOrOs!FIqvF;#"$,  qv.r#"A."A.)1% :S:#:$:,"c""2++R^^;< "2++R^^;<  %2++R^^;<% % %2++R^^;<% %2++R^^;<  $s)))112G8H-rxx78G G3G--556 8< M MXh'12 M!(!34 M  M7 M,%# .,,222r rOc ^\rSrSrSrSSS.S\S\S\S\\ \\ 4S S4 U4S jjjjr \ S \\4S j5r \SS\S \S\\ \\ 4S S4S jj5rS\ \R"\R$4S\R(S \R*4Sjr\"\R2R5S\ \\\R84S \R*4Sj5r\"\R:R5SS\S\ \\\R84S\\\S \R*4Sjj5r\ S \\S44Sj5rS \4Sjr Sr!U=r"$)CalendarTimeTrendia^ Constant and time trend determinstic terms based on calendar time Parameters ---------- freq : str A string convertible to a pandas frequency. constant : bool Flag indicating whether a constant should be included. order : int A non-negative int containing the powers to include (1, 2, ..., order). base_period : {str, pd.Timestamp}, default None The base period to use when computing the time stamps. This value is treated as 1 and so all other time indices are defined as the number of periods since or before this time stamp. If not provided, defaults to pandas base period for a PeriodIndex. See Also -------- DeterministicProcess CalendarFourier CalendarSeasonality TimeTrend Notes ----- The time stamp, :math:`\tau_t`, is the number of periods that have elapsed since the base_period. :math:`\tau_t` may be fractional. Examples -------- Here we simulate irregularly spaced hourly data and construct the calendar time trend terms for the data. >>> import numpy as np >>> import pandas as pd >>> base = pd.Timestamp("2020-1-1") >>> gen = np.random.default_rng() >>> gaps = np.cumsum(gen.integers(0, 1800, size=1000)) >>> times = [base + pd.Timedelta(gap, unit="s") for gap in gaps] >>> index = pd.DatetimeIndex(pd.to_datetime(times)) >>> from statsmodels.tsa.deterministic import CalendarTimeTrend >>> cal_trend_gen = CalendarTimeTrend("D", True, order=1) >>> cal_trend_gen.in_sample(index) Next, we normalize using the first time stamp >>> cal_trend_gen = CalendarTimeTrend("D", True, order=1, ... base_period=index[0]) >>> cal_trend_gen.in_sample(index) N base_periodrIrrrrc>[TU]U5 [RXUS9 SUlUb4[R "USUR S9nURSUlUcSUl g[U5Ul g)NrrrFrG) rrr_ref_i8r=rSr$asi8r} _base_period)rrIrrrprrs rrCalendarTimeTrend.__init__sw "++ 5 ,   "adjjIB771:DL$/$7DS=Mr cUR$)zThe base period)rrs rrCalendarTimeTrend.base_periods   r rcXURS5nSnSU;aSnOSU;aSnU"XXSS9$)aM Create a TimeTrend from a string description. Provided for compatibility with common string names. Parameters ---------- freq : str A string convertible to a pandas frequency. trend : {"n", "c", "t", "ct", "ctt"} The string representation of the time trend. The terms are: * "n": No trend terms * "c": A constant only * "t": Linear time trend only * "ct": A constant and a time trend * "ctt": A constant, a time trend and a quadratic time trend base_period : {str, pd.Timestamp}, default None The base period to use when computing the time stamps. This value is treated as 1 and so all other time indices are defined as the number of periods since or before this time stamp. If not provided, defaults to pandas base period for a PeriodIndex. Returns ------- TimeTrend The TimeTrend instance. rrrrJrrFrr)rrIrrrrs rrCalendarTimeTrend.from_strings?F##C( 5=E E\E45BBr r!rEcf[U[R5(aURUR5nUR nX0R - S-nUR[R5U-nUSS2S4nURU5n[R"XPRUS9$)NrFr) r<r=rTr.r$rrrrZrrr{r)rr!rEindex_i8timers r_termsCalendarTimeTrend._termss eR-- . .OODJJ/E::ll*Q.ryy)E1AtG}%||E==FFr cURU5nURU5nURU5nURX5$r1)rBr;r1r)rr!rEs rr%CalendarTimeTrend.in_samplesC  '&&u-##E*{{5((r r(r)cURU5nURX!U5nURU5 [U[R [R 45(deURU5nURXE5$r1) rBrer;r<r=rRrTr1r)rr(r!r)rrEs rr+CalendarTimeTrend.out_of_sample su  '((~F  {++8H8H'IJJJJ##K0{{;..r .cURURURR4nURbXR4- nU$r1)rrr$r)r)rattrs rr5CalendarTimeTrend._eq_attrsJ NN KK JJ  &     ( &&( (D r c[RU5nSUSS-SURRS3-nURbUSSSURS3-nU$)NCalendarrEz, freq=rz base_period=)rr.r$r)r)rvalues rr.CalendarTimeTrend.__str__&sl*2248U3BZ'GDJJ4F4F3Gq*II    (#2J<0A0A/B!!DDE r )rrrr1)#r3rurvrwrxr}rzr|r r DateLikerryrrrr=rTrRrZrr{rrrr%r r r>r+r~r5r.rrrs@rrrs3p N 7; NNN N eCM23 N NN$!Xc]!! 7; (C(C(CeCM23 (C  (C(CT G2++R^^;< GEGZZ G  G))112)8H-rxx78) )3)--556 8< / /Xh'12 /!(!34 /  /7 /%# .r rc\rSrSrSrSSSSSSSS.S\\\\R4S \ \\ \ 4S \ S \ S \ S \ S\\S\ 4Sjjr\S\R4Sj5r\S\\4Sj5rS\\R(S\\R(4SjrS\R(S\R(4Sjr\"\R0R5S\R(4Sj5r\"\R2R5S'S\ S\ \\\\R4S\R(4Sjj5rS\R4S\\R6\R844SjrS\ S\ S\R(4SjrS\R4S\R4S\R(4SjrS \ S!\ S\R44S"jr!S\\"\#\ 4S\\"\#\ 4S\R(4S#jr$S(S$jr%S%r&S&r'g))DeterministicProcessi.a\ Container class for deterministic terms. Directly supports constants, time trends, and either seasonal dummies or fourier terms for a single cycle. Additional deterministic terms beyond the set that can be directly initialized through the constructor can be added. Parameters ---------- index : {Sequence[Hashable], pd.Index} The index of the process. Should usually be the "in-sample" index when used in forecasting applications. period : {float, int}, default None The period of the seasonal or fourier components. Must be an int for seasonal dummies. If not provided, freq is read from index if available. constant : bool, default False Whether to include a constant. order : int, default 0 The order of the tim trend to include. For example, 2 will include both linear and quadratic terms. 0 exclude time trend terms. seasonal : bool = False Whether to include seasonal dummies fourier : int = 0 The order of the fourier terms to included. additional_terms : Sequence[DeterministicTerm] A sequence of additional deterministic terms to include in the process. drop : bool, default False A flag indicating to check for perfect collinearity and to drop any linearly dependent terms. See Also -------- TimeTrend Seasonality Fourier CalendarTimeTrend CalendarSeasonality CalendarFourier Notes ----- See the notebook `Deterministic Terms in Time Series Models <../examples/notebooks/generated/deterministics.html>`__ for an overview. Examples -------- >>> from statsmodels.tsa.deterministic import DeterministicProcess >>> from pandas import date_range >>> index = date_range("2000-1-1", freq="M", periods=240) First a determinstic process with a constant and quadratic time trend. >>> dp = DeterministicProcess(index, constant=True, order=2) >>> dp.in_sample().head(3) const trend trend_squared 2000-01-31 1.0 1.0 1.0 2000-02-29 1.0 2.0 4.0 2000-03-31 1.0 3.0 9.0 Seasonal dummies are included by setting seasonal to True. >>> dp = DeterministicProcess(index, constant=True, seasonal=True) >>> dp.in_sample().iloc[:3,:5] const s(2,12) s(3,12) s(4,12) s(5,12) 2000-01-31 1.0 0.0 0.0 0.0 0.0 2000-02-29 1.0 1.0 0.0 0.0 0.0 2000-03-31 1.0 0.0 1.0 0.0 0.0 Fourier components can be used to alternatively capture seasonal patterns, >>> dp = DeterministicProcess(index, constant=True, fourier=2) >>> dp.in_sample().head(3) const sin(1,12) cos(1,12) sin(2,12) cos(2,12) 2000-01-31 1.0 0.000000 1.000000 0.000000 1.0 2000-02-29 1.0 0.500000 0.866025 0.866025 0.5 2000-03-31 1.0 0.866025 0.500000 0.866025 -0.5 Multiple Seasonalities can be captured using additional terms. >>> from statsmodels.tsa.deterministic import Fourier >>> index = date_range("2000-1-1", freq="D", periods=5000) >>> fourier = Fourier(period=365.25, order=1) >>> dp = DeterministicProcess(index, period=3, constant=True, ... seasonal=True, additional_terms=[fourier]) >>> dp.in_sample().head(3) const s(2,3) s(3,3) sin(1,365.25) cos(1,365.25) 2000-01-01 1.0 0.0 0.0 0.000000 1.000000 2000-01-02 1.0 1.0 0.0 0.017202 0.999852 2000-01-03 1.0 0.0 1.0 0.034398 0.999408 NFrr#rrrseasonalfourieradditional_termsdropr!rrrrrrrcl[U[R5(d[R"U5nXl/UlSUlSUlUR5 [USSS9n[US5=Ul n[US5Ul [US5=Ul n[US5Ul[U5nSUl[US 5UlXplU(dU(a$URR'[)X455 U(aU(a [+S 5eU(dU(a"UcUc[-UR 5=UlnU(a1[US5nURR'[1U55 O:U(a3[US5nUceURR'[3X&S 95 UHXn [U [45(d [7S 5eXR;aURR'U 5 MO[+S 5e X lSUlg)NFrT)optionalrrrrrzseasonal and fourier can be initialized through the constructor since these will be necessarily perfectly collinear. Instead, you can pass additional components using the additional_terms input.)rzJAll additional terms must be instances of subsclasses of DeterministicTermzuOne or more terms in additional_terms has been added through the parameters of the constructor. Terms must be unique.)r<r=r>_index_deterministic_terms _extendable _index_freq_validate_indexrrrrr _seasonal_fourierr~_cached_in_sample_drop_additional_termsrrrQrrrrrr@ _retain_cols) rr!rrrrrrrrs rrDeterministicProcess.__init__s%**HHUOE =?!  FHt<$-h $CC'w7 $-h $CC)'9=  !12!%tV, !1 u  % % , ,Yx-G H H  V^~(6t7G7G(HH v &vx8F  % % , ,[-@ A 1F% %%  % % , ,WV-K L$Dd$566+444))006 !% 6:r rcUR$)zThe index of the process)rrs rr!DeterministicProcess.indexrr cUR$)z/The deterministic terms included in the process)rrs rrDeterministicProcess.termss(((r rcSnURH5n[U[[45(dM U=(d URnM7 UcVSnUHNnXDR S:HR 5UR SS:g-nU=(d UR5nMP Un[UR5HCupsURnU(a U(aXR SS2SS24X'U=(d UnME U$)NFrrF) rr<rrrilocr[anyrr) rr has_constdtermr const_col drop_firstrrs r_adjust_dummies$DeterministicProcess._adjust_dummiess$( ..E%)->!?@@%7 /  I!YYq\1668DIIaLAS!2!23 3++,E r rWcURn[U[R5(a"[R"USXR S9$[R "USXRS9$)Nr)endrI)rbrrI)rr<r=rRrSrIrUr)rrWr!s r_extend_time_index'DeterministicProcess._extend_time_index1sR  eR^^ , ,??58JJG G}}58r]r%rr+rPr)rrbrWr!is_int64_indexidx_stepnew_idxr% next_valuetmpoos in_sample_loc in_sample_idxout_of_sample_idxin_sample_exogoos_exogs r_range_from_range_index,DeterministicProcess._range_from_range_index:s %e,%//>AA 8 34 4 eR]] + +zzH/25zA~rwwu~))+1H q=uQx/8;A>xjI**  hhryy56GmmEh?G 2;$++b/ )(I! g.I  QZ$++b/ )rX-JqzZ'mmJ8D((1c(Jwww''%%gmmA&6w%O O;;r?2 . #N3)--m<%%#))!,=N& yy.3!<> 2 2%..T-=-=>$ --~~4+;+;~< 8 34 4 ;;r? ">>#''3 3))$/E"I-.  q!17; AJ 775& &yy$..*C0q9xx##r rr6cUS:a[US35eXRRS:aURU$XRRSS- - S-nURn[UR[R 5(a6[R "USURUS9nUSR5$[R"USURUS9nUS$)Nrz must be non-negative.rFrErK) rQrrPr<r=rRrSrr-rU)rrr6 add_periodsr!rdrs r_int_to_timestamp&DeterministicProcess._int_to_timestampzs 19v%;<= = ;;$$Q' ';;u% %{{003a781<   dkk2>> 2 2b  0 0+Bb6&&( ( ]] "ID,,k "v r ctUR(d [S5e[UR5[R 4;d[ UR5(a.[US5n[US5nUS- nURX5$[U[[R45(aURUS5nO[R"U5n[U[[R45(aURUS5nO[R"U5nURX5$)a Deterministic terms spanning a range of observations Parameters ---------- start : {int, str, dt.datetime, pd.Timestamp, np.datetime64} The first observation. stop : {int, str, dt.datetime, pd.Timestamp, np.datetime64} The final observation. Inclusive to match most prediction function in statsmodels. Returns ------- DataFrame A data frame of deterministic terms zThe index in the deterministic process does not support extension. Only PeriodIndex, DatetimeIndex with a frequency, RangeIndex, and integral Indexes that start at 0 and have only unit differences can be extended when producing out-of-sample forecasts. rbrWrF)rr@r2rr=rVrrrr<r|rZintegerr rr)rrbrWs rrDeterministicProcess.ranges*    0 0L4M4M%eW5E$T62D AID//< < ec2::. / /**5':ELL'E dS"**- . .))$7D<<%D**577r c[UR[R5(a#URRUlSUlg[UR[R5(aLURR=(d URRUlUR SLUlg[UR[R5(aSUlg[UR5(aVURSS:H=(a7 [R"[R"UR5S:H5Ulgg)NTrrF)r<rr=rRrIrrrTrrVrrZr[r\rs rr$DeterministicProcess._validate_indexs dkk2>> 2 2#{{//D #D   R%5%5 6 6#{{//L4;;3L3LD #//t;D   R]] 3 3#D  $++ & &#{{1~2 rvv $)8D 'r c [UURURURURUR UR URS9$)a Create an identical determinstic process with a different index Parameters ---------- index : index_like An index-like object. If not an index, it is converted to an index. Returns ------- DeterministicProcess The deterministic process applied to a different index r)rrrrrrrrr$s rapplyDeterministicProcess.applysG$ <<^^++^^MM!33  r ) rrrrrrrrrrrrrr1)rN)(r3rurvrwrxr r r r=r>r r r|rzrrryr!rrr{rrrr%r+rrTrRrrrr}r IntLikerrrr(rr#r rrr.s[B/38:=;Xh'12=;ucz*+ =;  =;  =;=;=;##45=;=;~rxx)t-.))T",,%7DrOrrr#r rr8s%$"., 4 bllBMM9 : RZZ  KK\/)!2C/)dW+*W+tCL#CLL0#(YF&YFx1 131h]J/1I]J@t23t2nl13Ml^p p r