Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 21.28% per annum.
- DD price at the close of February 14, 2020 was $53.10 and was lower than the bottom border of the primary price channel by $2.27 (4.09%).
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 62.24% per annum.
- DD price at the close of February 14, 2020 was inside the secondary price channel.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of DD price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: October 5, 2017
End date: January 29, 2020
a = 5.3212
b = -0.0007
s = 0.0562
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0007) – 1
= -21.28%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0562) – 1
= 25.21%
October 5, 2017 calculations
Top border of price channel:
Exp(Y665)
= Exp(a + b × X665 + 2 × s)
= Exp(a + b × 961 + 2 × s)
= Exp(5.3212 + -0.0007 × 961 + 2 × 0.0562)
= Exp(4.8038)
= $121.97
Bottom border of price channel:
Exp(Y665)
= Exp(a + b × X665 – 2 × s)
= Exp(a + b × 961 – 2 × s)
= Exp(5.3212 + -0.0007 × 961 – 2 × 0.0562)
= Exp(4.5790)
= $97.41
January 29, 2020 calculations
Top border of price channel:
Exp(Y1,246)
= Exp(a + b × X1,246 + 2 × s)
= Exp(a + b × 1,807 + 2 × s)
= Exp(5.3212 + -0.0007 × 1,807 + 2 × 0.0562)
= Exp(4.2493)
= $70.05
Bottom border of price channel:
Exp(Y1,246)
= Exp(a + b × X1,246 – 2 × s)
= Exp(a + b × 1,807 – 2 × s)
= Exp(5.3212 + -0.0007 × 1,807 – 2 × 0.0562)
= Exp(4.0245)
= $55.95
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 21.28% per annum.
- DD price at the close of February 14, 2020 was $53.10 and was lower than the bottom border of the primary price channel by $2.27 (4.09%).
Secondary Trend
Start date: November 1, 2019
End date: February 14, 2020
a = 8.8564
b = -0.0027
s = 0.0353
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0027) – 1
= -62.24%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0353) – 1
= 15.17%
November 1, 2019 calculations
Top border of price channel:
Exp(Y1,187)
= Exp(a + b × X1,187 + 2 × s)
= Exp(a + b × 1,718 + 2 × s)
= Exp(8.8564 + -0.0027 × 1,718 + 2 × 0.0353)
= Exp(4.3423)
= $76.89
Bottom border of price channel:
Exp(Y1,187)
= Exp(a + b × X1,187 – 2 × s)
= Exp(a + b × 1,718 – 2 × s)
= Exp(8.8564 + -0.0027 × 1,718 – 2 × 0.0353)
= Exp(4.2011)
= $66.76
February 14, 2020 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(8.8564 + -0.0027 × 1,823 + 2 × 0.0353)
= Exp(4.0621)
= $58.10
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(8.8564 + -0.0027 × 1,823 – 2 × 0.0353)
= Exp(3.9209)
= $50.45
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 62.24% per annum.
- DD price at the close of February 14, 2020 was inside the secondary price channel.
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