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 68.44% per annum.
- ISRG price at the close of February 20, 2025 was $606.57 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 57.97% per annum.
- ISRG price at the close of February 20, 2025 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: September 7, 2023
End date: February 20, 2025
a = 3.7945
b = 0.0014
s = 0.0479
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0014) – 1
= 68.44%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0479) – 1
= 21.12%
September 7, 2023 calculations
Top border of price channel:
Exp(Y892)
= Exp(a + b × X892 + 2 × s)
= Exp(a + b × 1,294 + 2 × s)
= Exp(3.7945 + 0.0014 × 1,294 + 2 × 0.0479)
= Exp(5.7388)
= $310.69
Bottom border of price channel:
Exp(Y892)
= Exp(a + b × X892 – 2 × s)
= Exp(a + b × 1,294 – 2 × s)
= Exp(3.7945 + 0.0014 × 1,294 – 2 × 0.0479)
= Exp(5.5472)
= $256.51
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(3.7945 + 0.0014 × 1,826 + 2 × 0.0479)
= Exp(6.4988)
= $664.34
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.7945 + 0.0014 × 1,826 – 2 × 0.0479)
= Exp(6.3072)
= $548.48
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 68.44% per annum.
- ISRG price at the close of February 20, 2025 was $606.57 and was inside the primary price channel.
Secondary Trend
Start date: January 10, 2024
End date: February 20, 2025
a = 4.0889
b = 0.0013
s = 0.0351
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0013) – 1
= 57.97%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0351) – 1
= 15.09%
January 10, 2024 calculations
Top border of price channel:
Exp(Y978)
= Exp(a + b × X978 + 2 × s)
= Exp(a + b × 1,419 + 2 × s)
= Exp(4.0889 + 0.0013 × 1,419 + 2 × 0.0351)
= Exp(5.9366)
= $378.66
Bottom border of price channel:
Exp(Y978)
= Exp(a + b × X978 – 2 × s)
= Exp(a + b × 1,419 – 2 × s)
= Exp(4.0889 + 0.0013 × 1,419 – 2 × 0.0351)
= Exp(5.7961)
= $329.01
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.0889 + 0.0013 × 1,826 + 2 × 0.0351)
= Exp(6.4465)
= $630.46
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.0889 + 0.0013 × 1,826 – 2 × 0.0351)
= Exp(6.3059)
= $547.81
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 57.97% per annum.
- ISRG price at the close of February 20, 2025 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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