Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 0.32% per annum.
- BDX price at the close of May 5, 2022 was $259.64 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 6.58% per annum.
- BDX price at the close of May 5, 2022 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 BDX 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: June 22, 2018
End date: January 7, 2022
a = 5.4756
b = 0.0000
s = 0.0492
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= 0.32%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0492) – 1
= 21.74%
June 22, 2018 calculations
Top border of price channel:
Exp(Y284)
= Exp(a + b × X284 + 2 × s)
= Exp(a + b × 410 + 2 × s)
= Exp(5.4756 + 0.0000 × 410 + 2 × 0.0492)
= Exp(5.5776)
= $264.43
Bottom border of price channel:
Exp(Y284)
= Exp(a + b × X284 – 2 × s)
= Exp(a + b × 410 – 2 × s)
= Exp(5.4756 + 0.0000 × 410 – 2 × 0.0492)
= Exp(5.3809)
= $217.22
January 7, 2022 calculations
Top border of price channel:
Exp(Y1,177)
= Exp(a + b × X1,177 + 2 × s)
= Exp(a + b × 1,705 + 2 × s)
= Exp(5.4756 + 0.0000 × 1,705 + 2 × 0.0492)
= Exp(5.5890)
= $267.48
Bottom border of price channel:
Exp(Y1,177)
= Exp(a + b × X1,177 – 2 × s)
= Exp(a + b × 1,705 – 2 × s)
= Exp(5.4756 + 0.0000 × 1,705 – 2 × 0.0492)
= Exp(5.3924)
= $219.72
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 0.32% per annum.
- BDX price at the close of May 5, 2022 was $259.64 and was inside the primary price channel.
Secondary Trend
Start date: September 3, 2020
End date: May 5, 2022
a = 5.2281
b = 0.0002
s = 0.0334
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0002) – 1
= 6.58%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0334) – 1
= 14.31%
September 3, 2020 calculations
Top border of price channel:
Exp(Y838)
= Exp(a + b × X838 + 2 × s)
= Exp(a + b × 1,214 + 2 × s)
= Exp(5.2281 + 0.0002 × 1,214 + 2 × 0.0334)
= Exp(5.5070)
= $246.41
Bottom border of price channel:
Exp(Y838)
= Exp(a + b × X838 – 2 × s)
= Exp(a + b × 1,214 – 2 × s)
= Exp(5.2281 + 0.0002 × 1,214 – 2 × 0.0334)
= Exp(5.3733)
= $215.56
May 5, 2022 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(5.2281 + 0.0002 × 1,823 + 2 × 0.0334)
= Exp(5.6134)
= $274.07
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(5.2281 + 0.0002 × 1,823 – 2 × 0.0334)
= Exp(5.4796)
= $239.76
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 6.58% per annum.
- BDX price at the close of May 5, 2022 was inside the secondary price channel.
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