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 3.81% per annum.
- ABBV price at the close of May 17, 2024 was $166.42 and was higher than the top border of the primary price channel by $1.12 (0.68%).
- The secondary trend is increasing.
- The growth rate of the secondary trend is 39.36% per annum.
- ABBV price at the close of May 17, 2024 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 ABBV 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: December 27, 2021
End date: December 29, 2023
a = 4.8070
b = 0.0001
s = 0.0570
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 3.81%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0570) – 1
= 25.59%
December 27, 2021 calculations
Top border of price channel:
Exp(Y657)
= Exp(a + b × X657 + 2 × s)
= Exp(a + b × 952 + 2 × s)
= Exp(4.8070 + 0.0001 × 952 + 2 × 0.0570)
= Exp(5.0184)
= $151.17
Bottom border of price channel:
Exp(Y657)
= Exp(a + b × X657 – 2 × s)
= Exp(a + b × 952 – 2 × s)
= Exp(4.8070 + 0.0001 × 952 – 2 × 0.0570)
= Exp(4.7906)
= $120.37
December 29, 2023 calculations
Top border of price channel:
Exp(Y1,162)
= Exp(a + b × X1,162 + 2 × s)
= Exp(a + b × 1,684 + 2 × s)
= Exp(4.8070 + 0.0001 × 1,684 + 2 × 0.0570)
= Exp(5.0934)
= $162.94
Bottom border of price channel:
Exp(Y1,162)
= Exp(a + b × X1,162 – 2 × s)
= Exp(a + b × 1,684 – 2 × s)
= Exp(4.8070 + 0.0001 × 1,684 – 2 × 0.0570)
= Exp(4.8655)
= $129.74
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 3.81% per annum.
- ABBV price at the close of May 17, 2024 was $166.42 and was higher than the top border of the primary price channel by $1.12 (0.68%).
Secondary Trend
Start date: May 23, 2023
End date: April 25, 2024
a = 3.5252
b = 0.0009
s = 0.0484
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0009) – 1
= 39.36%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0484) – 1
= 21.37%
May 23, 2023 calculations
Top border of price channel:
Exp(Y1,010)
= Exp(a + b × X1,010 + 2 × s)
= Exp(a + b × 1,464 + 2 × s)
= Exp(3.5252 + 0.0009 × 1,464 + 2 × 0.0484)
= Exp(4.9531)
= $141.62
Bottom border of price channel:
Exp(Y1,010)
= Exp(a + b × X1,010 – 2 × s)
= Exp(a + b × 1,464 – 2 × s)
= Exp(3.5252 + 0.0009 × 1,464 – 2 × 0.0484)
= Exp(4.7594)
= $116.68
April 25, 2024 calculations
Top border of price channel:
Exp(Y1,242)
= Exp(a + b × X1,242 + 2 × s)
= Exp(a + b × 1,802 + 2 × s)
= Exp(3.5252 + 0.0009 × 1,802 + 2 × 0.0484)
= Exp(5.2605)
= $192.57
Bottom border of price channel:
Exp(Y1,242)
= Exp(a + b × X1,242 – 2 × s)
= Exp(a + b × 1,802 – 2 × s)
= Exp(3.5252 + 0.0009 × 1,802 – 2 × 0.0484)
= Exp(5.0667)
= $158.66
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 39.36% per annum.
- ABBV price at the close of May 17, 2024 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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