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 44.95% per annum.
- ISRG price at the close of November 19, 2024 was $538.82 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 72.40% per annum.
- ISRG price at the close of November 19, 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 ISRG 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 3, 2022
End date: November 19, 2024
a = 4.3452
b = 0.0010
s = 0.0848
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0010) – 1
= 44.95%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0848) – 1
= 40.37%
June 3, 2022 calculations
Top border of price channel:
Exp(Y638)
= Exp(a + b × X638 + 2 × s)
= Exp(a + b × 926 + 2 × s)
= Exp(4.3452 + 0.0010 × 926 + 2 × 0.0848)
= Exp(5.4565)
= $234.28
Bottom border of price channel:
Exp(Y638)
= Exp(a + b × X638 – 2 × s)
= Exp(a + b × 926 – 2 × s)
= Exp(4.3452 + 0.0010 × 926 – 2 × 0.0848)
= Exp(5.1174)
= $166.90
November 19, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.3452 + 0.0010 × 1,826 + 2 × 0.0848)
= Exp(6.3719)
= $585.16
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.3452 + 0.0010 × 1,826 – 2 × 0.0848)
= Exp(6.0327)
= $416.85
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 44.95% per annum.
- ISRG price at the close of November 19, 2024 was $538.82 and was inside the primary price channel.
Secondary Trend
Start date: September 20, 2023
End date: November 19, 2024
a = 3.5596
b = 0.0015
s = 0.0498
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0015) – 1
= 72.40%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0498) – 1
= 22.03%
September 20, 2023 calculations
Top border of price channel:
Exp(Y963)
= Exp(a + b × X963 + 2 × s)
= Exp(a + b × 1,400 + 2 × s)
= Exp(3.5596 + 0.0015 × 1,400 + 2 × 0.0498)
= Exp(5.7483)
= $313.65
Bottom border of price channel:
Exp(Y963)
= Exp(a + b × X963 – 2 × s)
= Exp(a + b × 1,400 – 2 × s)
= Exp(3.5596 + 0.0015 × 1,400 – 2 × 0.0498)
= Exp(5.5492)
= $257.04
November 19, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(3.5596 + 0.0015 × 1,826 + 2 × 0.0498)
= Exp(6.3840)
= $592.28
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.5596 + 0.0015 × 1,826 – 2 × 0.0498)
= Exp(6.1849)
= $485.37
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 72.40% per annum.
- ISRG price at the close of November 19, 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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