Time-Series

分析 ACF 和 PACF 圖

  • January 22, 2015

我想看看我是否在分析我的 ACF 和 PACF 圖的正確軌道上:

在此處輸入圖像描述

背景:(參考:Philip Hans Franses,1998)

  1. 由於 ACF 和 PACF 都顯示出重要的價值,我假設 ARMA 模型將滿足我的需求
  2. ACF可以用來估計MA-part,即q-value,PACF可以用來估計AR-part,即p-value
  3. 為了估計模型順序,我查看 a.) ACF 值是否充分消失,b.) ACF 信號是否過度差異以及 c.) ACF 和 PACF 是否在某些滯後處顯示任何顯著且易於解釋的峰值
  4. ACF 和 PACF 可能不僅建議一種模型,而且在考慮其他診斷工具後我需要從中選擇許多模型

考慮到這一點,我會繼續說最明顯的模型似乎是 ARMA (4,2),因為 ACF 值在滯後 4 處消失,而 PACF 在 1 和 2 處顯示峰值。

另一種分析方法是 ARMA(2,1),因為我看到我的 PACF 中有兩個顯著峰值,我的 ACF 中有一個顯著峰值(之後值從低得多的點 (0.4) 開始消失)。

查看我的樣本內預測結果(使用簡單的平均絕對百分比誤差)ARMA (2,1) 提供的結果要好於 ARMA(4,2)。所以我使用 ARMA(2,1)!

你能證實我分析 ACF 和 PACF 圖的方法和發現嗎?

幫助表示讚賞!

編輯:

描述性統計:

count  252.000000
mean    29.576151
std      7.817171
min     -0.920000
25%     26.877500
50%     30.910000
75%     34.915000
max     47.430000

Skewness of endog_var: [-1.35798399]

Kurtsosis of endog_var: [ 5.4917757]

Augmented Dickey-Fuller Test for endog_var: (-3.76140904255411, 0.0033277703768345287, {'5%': -2.8696473721448728, '1%': -3.4487489051519011, '10%': -2.5710891239349585}

時間序列:

在此處輸入圖像描述

殘差 (ARMA (2.1):

在此處輸入圖像描述

殘差的 ACF/PACF:

在此處輸入圖像描述

編輯二:

數據:

14.37561
23.95561
25.41561
13.88561
23.31561
33.12561
35.30561
35.78561
37.21561
35.23561
37.34561
38.28561
39.03561
36.34561
39.08561
39.34561
38.80561
40.10561
34.13561
35.42561
27.29561
34.13561
39.89561
47.77561
40.57561
36.15561
33.66561
30.97561
24.90561
23.41561
0.31561
8.45561
37.36561
33.40561
13.97561
11.62561
35.07561
36.15561
37.09561
36.95561
37.85561
32.31561
35.41561
36.35561
37.34561
35.90561
37.40561
36.44561
37.37561
36.16561
35.24561
38.47561
39.18561
39.61561
29.55561
35.50561
38.05561
40.32561
44.39561
37.65561
46.27561
29.41561
40.41561
33.44561
37.04561
35.34561
25.24561
30.23561
15.40561
26.79561
35.38561
40.22561
43.14561
36.96561
41.93561
11.30561
6.87561
32.92561
34.54561
38.27561
36.40561
25.44561
37.26561
26.39561
31.13561
35.90561
38.41561
33.66561
33.16561
31.96561
30.34561
37.77561
32.25561
33.21561
38.37561
36.63561
40.78561
35.60561
36.37561
34.42561
42.67561
33.40561
31.49561
24.81561
23.82561
37.34561
30.73561
21.04561
18.20561
27.36561
18.49561
25.41561
27.92561
29.42561
25.91561
27.56561
28.69561
29.89561
31.47561
29.34561
25.35561
21.98561
28.61561
33.87561
20.07561
27.36561
26.48561
20.37561
22.33561
28.52561
21.24561
10.77561
18.69561
30.19561
33.89561
29.81561
27.55561
22.37561
20.32561
22.43561
31.89561
32.10561
27.67561
36.93561
36.51561
26.96561
21.27561
34.68561
34.13561
35.80561
25.38561
33.42561
9.28561
8.70561
30.36561
30.29561
29.56561
28.41561
33.40561
18.47561
16.48561
18.51561
26.35561
25.40561
19.92561
21.26561
10.90561
32.71561
26.71561
29.99561
28.87561
28.55561
14.07561
10.97561
24.92561
26.40561
21.40561
29.08561
30.18561
30.27561
16.15561
21.96561
32.29561
29.57561
30.24561
30.82561
28.83561
27.30561
26.53561
28.39561
29.76561
29.50561
31.81561
34.79561
24.14561
31.34561
33.14561
35.04561
33.20561
33.53561
35.28561
29.84561
35.02561
33.63561
35.65561
35.73561
35.35561
37.18561
27.38561
34.40561
33.69561
29.05561
34.55561
31.76561
30.91561
34.70561
35.87561
28.31561
30.39561
28.03561
30.72561
30.57561
23.93561
25.11561
32.15561
26.74561
28.76561
32.49561
34.79561
27.90561
33.05561
29.50561
31.67561
34.36561
36.88561
32.31561
26.24561
26.66561
33.59561
37.64561
38.26561
36.20561
33.27561
29.94561
29.19561
27.41561
37.24561
36.26561
30.84561
35.46561
32.24561
31.44561
33.40561
30.71561
33.03561
36.43561
33.44561
22.32561
18.65561
31.97561
27.00561
29.66561
30.76561
33.44561
29.19561
12.32561
33.41561
37.13561
33.43561
37.35561
40.17561
29.38561
19.70561
35.44561
30.48561
30.72561
16.09561
30.82561
30.55561
34.38561
35.45561
34.87561
33.78561
33.87561
29.83561
26.35561
26.44561
28.72561
30.85561
28.18561
12.18561
31.82561
18.01561
27.57561
29.38561
20.32561
22.36561
34.01561
34.40561
20.23561
-0.57439
9.87561
29.55561
31.01561
30.00561
28.12561
13.47561
7.42561
22.01561
20.38561
27.57561
31.54561
29.90561
16.40561
21.27561
26.22561
31.47561
31.11561
32.97561
32.34561
29.36561
32.40561
31.16561
32.05561
31.78561
32.34561
33.87561
31.80561
29.90561
30.09561
32.36561
28.15561
26.30561
15.32561
31.03561
33.47561
33.44561
33.71561
28.30561
12.70561
10.17561
43.96561
9.58561
35.38561
33.82561
41.37561
33.40561
33.64561
20.30561
27.85561
29.01561
32.36561
28.33561
29.90561
27.19561
0.39561
8.40561
0.24561
11.87561
29.15561
20.40561
0.42561
29.29561
23.39561
19.36561

查看您的 ACF 和 PACF 在您的分析的完整上下文中也很有用。你的 Ljung-Box Q 統計量;p 值;置信區間、ACF 和 PACF 應一起查看。例如這裡的 Q 測試:

acf, ci, Q, pvalue = tsa.acf(res1.resid, nlags=4,confint=95,  qstat=True, unbiased=True)

在這裡 - 我們的自相關 Q 檢驗是對我們的圖形解釋的整體直覺檢查。

Statsmodels 中時間序列分析的草稿說明:http: //conference.scipy.org/proceedings/scipy2011/pdfs/statsmodels.pdf

引用自:https://stats.stackexchange.com/questions/134487

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