I have 2 time series sampled at a weekly level spanning a period from the start of 2010 until the present. Initially I had used a TBATS model with the frequency of the time series set to 52. This looked to give sensible results, but I figured, since TBATS can handle non-integer frequencies, I should change the frequency to 365.25 / 7 = 52.17857 as is done here.
When I did this I noticed the forecasts seemed a bit off, and when I checked the decomposition I noticed the level was fluctuating heavily for one of the time series. The season component had stayed comparable, albeit more jagged, but the level component had gone from slow changes with a range of 850-700 to jumps up and down with a range of 1400-400.
The two series are very similar to each other but the decomposition of the second series didn't change much with the frequency change. Below are the decompositions of both series at both frequency levels.
What is going on here and is this something I should worry about? Is it a bug/oddity in the specific implementation (forecast package in R)?
dput of the first series in R:
structure(c(926.915, 923.497, 916.97, 911.267, 894.965, 936.03,
962.102, 918.534, 899.158, 878.569, 901.717, 848.169, 870.812,
864.669, 840.871, 810.228, 846.338, 832.886, 849.071, 734.825,
852.511, 756.261, 884.513, 885.06, 799.502, 816.897, 799.618,
656.528, 685.403, 684.381, 708.81, 751.779, 722.581, 812.192,
823.693, 832.619, 832.628, 836.887, 879.466, 875.132, 905.392,
897.43, 900.862, 891.022, 906.717, 892.422, 893.856, 905.742,
909.633, 938.824, 904.886, 939.096, 945.762, 929.112, 920.017,
909.707, 913.35, 914.074, 899.561, 909.283, 900.81, 937.34, 901.83,
864.466, 868.084, 843.824, 839.266, 731.042, 851.415, 785.762,
860.109, 788.867, 825.761, 749.09, 789.731, 794.412, 734.27,
743.961, 733.326, 784.091, 754.418, 624.366, 701.648, 729.34,
704.723, 776.66, 761.43, 826.768, 853.651, 816.424, 800.577,
883.538, 868.67, 894.388, 900.545, 916.244, 918.758, 932.134,
897.096, 909.416, 882.704, 891.794, 836.364, 908.222, 922.486,
900.1, 913.606, 901.255, 937.755, 939.635, 901.92, 907.393, 899.676,
892.542, 893.305, 845.017, 866.149, 876.966, 875.355, 860.649,
818.936, 839.306, 805.966, 791.747, 661.655, 797.807, 951.996,
940.786, 809.329, 759.465, 690.255, 701.883, 596.631, 658.932,
717.371, 683.504, 595.816, 732.638, 798.835, 785.196, 840.206,
855.929, 829.165, 857.499, 867.691, 872.909, 873.255, 899.258,
893.324, 914.27, 892.57, 869.015, 886.114, 887.402, 863.978,
921.455, 934.61, 933.106, 931.889, 944.748, 918.227, 926.489,
924.202, 922.751, 897.307, 923.338, 915.47, 886.166, 883.631,
888.522, 847.895, 867.383, 834.154, 773.028, 847.63, 884.73,
802.519, 758.384, 703.777, 738.002, 740.357, 742.313, 622.798,
609.309, 543.778, 596.921, 555.572, 667.107, 700.175, 707.479,
761.604, 780.935, 837.426, 830.736, 844.079, 855.158, 869.613,
888.677, 874.521, 894.321, 922.937, 893.846, 891.64, 865.055,
886.57, 884.672, 902.061, 910.966, 955.651, 909.796, 904.644,
899.37, 885.442, 955.921, 932.548, 916.509, 869.903, 856.328,
877.257, 864.619, 807.412, 824.67, 846.705, 849.513, 818.807,
828.191, 863.915, 750.247, 776.783, 761.862, 702.669, 881.275,
1013.397, 934.235, 838.026, 800.756, 592.093, 620.494, 572.609,
681.978, 722.117, 762.134, 754.935, 782.035, 798.123, 812.046,
820.237, 845.082, 863.147, 886.343, 869.119, 867.556, 898.197,
902.843, 883.258, 894.563, 873.212, 884.96, 898.658, 900.794,
967.284, 926.981, 900.286, 882.893, 898.942, 876.08, 864.506,
877.199, 879.171, 849.551, 851.75, 848.133, 863.232, 832.545,
792.919, 782.858, 778.714, 791.807, 757.866, 804.322, 753.782,
769.116, 690.172, 670.608, 724.423, 597.289, 589.338, 677.806,
619.553, 639.56, 562.82, 520.034, 632.719, 646.474, 693.41, 770.842,
747.413, 778.006, 767.218, 798.232, 818.956, 815.431, 799.765,
801.209, 818.282, 841.303, 818.749, 809.258, 788.346, 805.102,
787.675, 790.079, 892.197, 838.152, 832.562, 814.102, 810.305,
796.506, 836.003, 829.5, 803.115, 828.306, 779.218, 776.303,
770.855, 727.182, 733.368, 705.507, 721.247, 709.431, 615.091,
690.494, 702.825, 662.401, 630.707, 717.418, 725.443), .Dim = c(337L,
1L), .Dimnames = list(NULL, structure("Total", .Names = "Level 0")), .Tsp = c(1,
7.43942522763656, 52.17857), class = "ts")
