kalmanSSM: Univariate State Space Model Data

Ivan Jacob Agaloos Pesigan

library(kalmanSSM)

Model Generating Model

Measurement Model

\[\begin{equation} Y = \eta + \varepsilon \quad \text{with} \quad \mathcal{N} \left( 0, 1 \right) \end{equation}\]

Dynamic Model

\[\begin{equation} \eta_{t} = 0.8 \eta_{t - 1} + \zeta_{t} \quad \text{with} \quad \mathcal{N} \left( 0, 1 \right) \end{equation}\]

Data

knitr::kable(dat_univ_p1)

eta	y	time
1.3709584	0.8062603	1
1.4598952	2.0927578	2
1.5721845	1.4660599	3
2.7692696	2.6746105	4
4.2338394	4.1711253	5
4.6919411	6.9785865	6
2.3646922	2.0859034	7
1.7584324	2.3943828	8
1.1224930	-1.5339624	9
-1.5424725	-0.2223592	10
-1.5406166	-3.3219250	11
-1.4044106	-0.1897359	12
0.7716650	0.3411958	13
0.3600626	-1.4031005	14
0.7481474	0.1081525	15
1.0539681	1.7588054	16
1.8782780	1.2693516	17
2.0075775	0.2905688	18
0.8216030	-0.0293046	19
-1.7569253	-1.7208027	20
-1.1995416	-1.5605989	21
-0.2014700	-0.9281749	22
-1.5294571	-1.0966391	23
-2.0349588	-0.5908576	24
-2.0594133	-1.4037654	25
-1.3256054	-2.1094443	26
0.5152432	1.1581425	27
0.5019552	0.7785060	28
1.0808530	1.1706859	29
-2.1284077	-1.8435247	30
-2.0699608	-1.8847302	31
-1.0741449	0.3255919	32
-1.5866080	-0.2840653	33
-0.9334383	0.1050678	34
0.1739780	0.8948561	35
-0.9039366	-0.9941230	36
-0.0996311	-1.0531545	37
-0.6225337	-0.0415372	38
0.2701518	0.7339194	39
-0.6696549	-1.7694358	40
0.9769831	1.2349046	41
0.8700267	0.7491302	42
-0.4983075	0.1136894	43
-0.6157859	-0.7985426	44
0.4407176	1.2624908	45
1.7446905	1.2685166	46
2.0461010	3.4372114	47
0.5260919	-0.3347007	48
-0.7108652	-2.1700792	49
-0.4887096	0.1644948	50
0.8099977	1.8547488	51
-0.3552105	1.4932714	52
-0.9509418	-0.8454280	53
-1.1830093	-1.3053595	54
-0.7582144	-0.6390535	55
-0.6316641	-0.5235914	56
-0.9907665	-1.4949836	57
-2.4537123	-2.8360460	58
-2.4756201	0.2262709	59
-3.3426123	-3.2053561	60
-4.1677149	-5.6381506	61
-3.2094695	-4.2061087	62
-2.5693982	-2.9976571	63
-2.6691902	-4.6938680	64
-3.3601001	-3.1805837	65
-2.1204595	-2.6133368	66
-1.6963047	-0.5734151	67
0.0828120	-1.0143018	68
-0.0510700	1.1504284	69
-0.5105856	-0.5630551	70
-0.4945758	-1.3822548	71
-0.8403446	-0.8697895	72
-1.0861445	0.0272415	73
-1.3499085	-1.7830775	74
-0.3830642	-1.4394326	75
-0.3471498	-1.8986947	76
0.8894497	0.6158040	77
0.2437144	-0.9945379	78
0.1872095	-0.6130727	79
-0.3837247	0.9039505	80
-0.4825057	-1.5542880	81
-0.2227976	-0.5855361	82
0.4117754	1.8441974	83
-0.6632722	-0.2086219	84
-0.4457197	0.4498459	85
-0.5863539	0.2502652	86
-2.2141390	-0.5246800	87
-0.9065332	-1.0573092	88
-2.1742337	-1.5312250	89
-1.2561931	-1.2625487	90
-0.8534986	-1.4376075	91
-0.3139921	-0.0193378	92
-0.5304531	-1.8666897	93
0.2763864	0.8305830	94
-0.6151975	-2.2097857	95
-0.2871994	-0.6322874	96
0.0228522	-1.2711503	97
-0.9408887	0.1448861	98
-0.3489361	0.2375515	99
1.5360796	1.6649010	100

Plot