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 19.86% per annum.
- MRK price at the close of May 20, 2024 was $130.99 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 61.04% per annum.
- MRK price at the close of May 20, 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 MRK 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: January 27, 2021
End date: May 20, 2024
a = 3.9365
b = 0.0005
s = 0.0612
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0005) – 1
= 19.86%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0612) – 1
= 27.73%
January 27, 2021 calculations
Top border of price channel:
Exp(Y425)
= Exp(a + b × X425 + 2 × s)
= Exp(a + b × 617 + 2 × s)
= Exp(3.9365 + 0.0005 × 617 + 2 × 0.0612)
= Exp(4.3651)
= $78.66
Bottom border of price channel:
Exp(Y425)
= Exp(a + b × X425 – 2 × s)
= Exp(a + b × 617 – 2 × s)
= Exp(3.9365 + 0.0005 × 617 – 2 × 0.0612)
= Exp(4.1204)
= $61.58
May 20, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(3.9365 + 0.0005 × 1,826 + 2 × 0.0612)
= Exp(4.9652)
= $143.33
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.9365 + 0.0005 × 1,826 – 2 × 0.0612)
= Exp(4.7204)
= $112.21
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 19.86% per annum.
- MRK price at the close of May 20, 2024 was $130.99 and was inside the primary price channel.
Secondary Trend
Start date: September 29, 2023
End date: May 20, 2024
a = 2.5236
b = 0.0013
s = 0.0364
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0013) – 1
= 61.04%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0364) – 1
= 15.66%
September 29, 2023 calculations
Top border of price channel:
Exp(Y1,098)
= Exp(a + b × X1,098 + 2 × s)
= Exp(a + b × 1,592 + 2 × s)
= Exp(2.5236 + 0.0013 × 1,592 + 2 × 0.0364)
= Exp(4.6746)
= $107.19
Bottom border of price channel:
Exp(Y1,098)
= Exp(a + b × X1,098 – 2 × s)
= Exp(a + b × 1,592 – 2 × s)
= Exp(2.5236 + 0.0013 × 1,592 – 2 × 0.0364)
= Exp(4.5291)
= $92.67
May 20, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(2.5236 + 0.0013 × 1,826 + 2 × 0.0364)
= Exp(4.9800)
= $145.48
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(2.5236 + 0.0013 × 1,826 – 2 × 0.0364)
= Exp(4.8345)
= $125.78
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 61.04% per annum.
- MRK price at the close of May 20, 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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