Table 5.
Outlier detection with TRAMO in the Online_Retail time series (Jan 2000–Jan 2022)
| Country | OUT (1) | OUT (2) | OUT (3) | OUT (4) | OUT (5) | OUT (6) | OUT (7) | OUT (8) | OUT (9) | OUT (10) |
|---|---|---|---|---|---|---|---|---|---|---|
| EU-27 | TC (7–2021): −0.114 [-6.265] | TC (7–2020): −0.105 [-6.765] | LS (4–2020): 0.185 [12.005] | LS (5–2015): 0.096 [6.315] | AO (8–2009): −0.059 [-3.58] | AO (12–2005): 0.061 [3.696] | AO (6–2000): −0.05 [-3.031] | |||
| Belgium | LS (4–2020): 0.266 [5.77] | AO (11–2008): −0.313 [-6.097] | AO (7–2008): −0.46 [-9] | LS (1–2006): −0.54 [-11.719] | AO (5–2001): 0.501 [9.567] | AO (4–2001): 0.211 [4.054] | ||||
| Bulgaria | LS (1–2006): −0.269 [-4.574] | |||||||||
| Czechia | TC (4–2020): 0.19 [26.189] | TC (12–2019): 0.041 [5.591] | TC (8–2014): 0.136 [23.936] | LS (1–2013): 0.122 [19.92] | LS (12–2008): −0.144 [-23.536] | AO (5–2000): 0.454 [50.068] | ||||
| Denmark | LS (4–2020): 0.206 [6.138] | AO (5–2005): 0.155 [4.791] | AO (12–2004): −0.233 [-7.159] | AO (7–2004): 0.215 [6.429] | LS (1–2004): 0.218 [6.693] | AO (12–2001): 0.213 [6.548] | AO (8–2001): −0.195 [-5.809] | AO (7–2001): 0.253 [7.519] | AO (4–2001): 0.183 [5.625] | TC (2–2001): −0.299 [-8.764] |
| Germany | LS (7–2021): −0.149 [-6.325] | LS (4–2020): 0.214 [9.752] | LS (5–2015): 0.205 [10.089] | LS (1–2015): 0.05 [2.445] | AO (4–2008): 0.083 [3.917] | AO (9–2006): −0.096 [-4.46] | AO (12–2005): 0.114 [5.327] | AO (6–2000): −0.127 [-5.169] | AO (5–2000): 0.129 [5.24] | |
| Estonia | LS (1–2005): −0.391 [-4.776] | TC (8–2003): −0.308 [-3.892] | TC (8–2002): 0.31 [3.914] | |||||||
| Greece | AO (7–2015): −0.386 [-4.014] | AO (8–2008): −0.429 [-4.46] | LS (12–2004): −0.502 [-4.008] | |||||||
| Spain | AO (7–2021): −0.228 [-6.79] | AO (7–2020): −0.217 [-6.468] | LS (4–2020): 0.339 [8.35] | LS (5–2015): 0.225 [5.535] | LS (9–2012): −0.181 [-4.446] | AO (8–2001): 0.211 [6.289] | AO (2–2001): 0.401 [11.971] | |||
| France | TC (7–2021): −0.092 [-4.605] | TC (2–2021): 0.123 [6.796] | AO (7–2020): −0.219 [-14.341] | LS (5–2020): 0.167 [10.036] | AO (4–2017): −0.064 [-4.179] | LS (8–2015): 0.157 [9.461] | AO (8–2009): −0.06 [-3.929] | AO (4–2006): 0.07 [4.553] | AO (4–2005): 0.072 [4.705] | AO (11–2003): −0.09 [-5.91] |
| Croatia | AO (8–2020): −0.251 [-4.267] | AO (3–2020): −0.246 [-4.195] | AO (8–2019): −0.329 [-5.61] | TC (10–2014): −0.372 [-6.038] | TC (8–2014): 0.506 [8.207] | AO (7–2005): −0.286 [-4.868] | AO (2–2004): 0.306 [5.172] | AO (12–2003): −0.271 [-4.57] | AO (8–2003): −0.289 [-4.903] | LS (5–2003): −0.247 [-4.195] |
| Italy | AO (5–2021): −0.173 [-19.32] | LS (8–2020): 0.02 [3.615] | LS (5–2020): 0.011 [1.837] | AO (12–2018): −0.143 [-28.913] | TC (1–2014): 0.154 [44.932] | AO (1–2010): 0.126 [33.284] | ||||
| Lithuania | LS (7–2021): −30.487 [-13.656] | TC (3–2021): 25.141 [14.866] | LS (2–2021): 16.387 [7.689] | TC (12–2020): 111.835 [58.71] | LS (11–2020): 27.01 [13.7] | TC (6–2020): −14.646 [-8.642] | LS (4–2020): 90.59 [49.585] | TC (3–2020): 11.86 [6.659] | AO (11–2019): −14.275 [-12.237] | AO (4–2018): −9.764 [-8.765] |
| Hungary | TC (4–2020): 0.393 [10.824] | LS (7–2011): 0.197 [9.63] | AO (12–2007): 0.123 [5.93] | AO (9–2006): −0.026 [-1.293] | AO (1–2005): −0.041 [-2.035] | AO (8–2004): −0.078 [-3.728] | AO (12–2002): −0.147 [-5.766] | |||
| Netherlands | TC (1–2021): 0.19 [6.623] | LS (4–2020): 0.158 [6.298] | TC (2–2005): 0.262 [9.231] | AO (12–2004): −0.162 [-5.848] | TC (9–2004): 0.216 [7.467] | TC (1–2004): 0.179 [6.556] | AO (8–2002): 0.162 [5.963] | TC (9–2001): 0.162 [5.904] | AO (10–2000): −0.144 [-5.064] | LS (4–2000): 0.156 [5.577] |
| Austria | TC (11–2020): 0.173 [5.619] | LS (4–2020): 0.161 [6.573] | AO (7–2005): −0.124 [-3.734] | TC (4–2004): 0.131 [4.318] | ||||||
| Poland | LS (10–2013): −0.225 [-3.898] | LS (1–2010): 0.327 [5.663] | LS (1–2008): 0.44 [7.604] | LS (1–2006): 0.578 [10.001] | TC (6–2001): −0.253 [-4.441] | TC (10–2000): −0.266 [-4.664] | ||||
| Portugal | TC (5–2019): 0.321 [4.498] | LS (1–2005): −0.587 [-8.939] | TC (1–2001): 0.387 [5.425] | |||||||
| Romania | TC (1–2008): −1.589 [-38.435] | LS (12–2005): 1.346 [29.719] | AO (6–2005): 0.738 [19.879] | AO (1–2005): −1.199 [-28.919] | TC (11–2004): 0.396 [8.765] | LS (7–2004): 0.617 [10.883] | AO (9–2003): −0.296 [-8.396] | LS (1–2002): 0.295 [5.523] | LS (1–2001): 0.678 [12.269] | LS (7–2000): −0.4 [-7.31] |
| Finland | LS (4–2020): 0.259 [10.479] | |||||||||
| Sweden | LS (4–2020): 0.18 [9.191] | AO (5–2019): −0.078 [-3.674] | LS (4–2018): −0.175 [-8.951] | LS (1–2018): −0.075 [-3.803] | TC (12–2013): 0.076 [3.688] | AO (4–2006): 0.089 [4.183] | AO (12–2003): −0.113 [-5.36] | AO (12–2002): −0.101 [-4.745] | AO (10–2002): 0.083 [3.908] | AO (6–2001): 0.103 [4.869] |
| Norway | LS (6–2021): −0.2 [-7.072] | LS (2–2021): 0.132 [4.606] | LS (11–2020): 0.138 [4.863] | AO (4–2020): 0.161 [5.189] | LS (3–2020): 0.215 [7.412] | TC (12–2018): −0.141 [-4.648] | AO (9–2004): 0.123 [4.133] | LS (6–2001): −0.123 [-4.405] | ||
| United Kingdom | TC (5–2020): 0.147 [4.603] | LS (4–2020): 0.17 [5.772] | LS (12–2002): −0.139 [-5.252] | LS (2–2001): −0.178 [-6.737] | ||||||
| Turkey | AO (11–2019): 0.143 [4.528] | AO (11–2018): 0.176 [5.586] | TC (2–2014): −0.207 [-5.546] |
Content of cells: (a) type of outlier: LS – level shift, TC – transitory change, AO – Additive outlier; (b) month of occurrence in parentheses; (c) magnitude of outlier [t-value].